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1 | 2290-2293 | Energy is lost during this time in
the form of heat and electromagnetic radiation EXAMPLE 2 10
SUMMARY
1 Electrostatic force is a conservative force |
1 | 2291-2294 | EXAMPLE 2 10
SUMMARY
1 Electrostatic force is a conservative force Work done by an external
force (equal and opposite to the electrostatic force) in bringing a charge
q from a point R to a point P is q(VP–VR), which is the difference in
potential energy of charge q between the final and initial points |
1 | 2292-2295 | 10
SUMMARY
1 Electrostatic force is a conservative force Work done by an external
force (equal and opposite to the electrostatic force) in bringing a charge
q from a point R to a point P is q(VP–VR), which is the difference in
potential energy of charge q between the final and initial points 2 |
1 | 2293-2296 | Electrostatic force is a conservative force Work done by an external
force (equal and opposite to the electrostatic force) in bringing a charge
q from a point R to a point P is q(VP–VR), which is the difference in
potential energy of charge q between the final and initial points 2 Potential at a point is the work done per unit charge (by an external
agency) in bringing a charge from infinity to that point |
1 | 2294-2297 | Work done by an external
force (equal and opposite to the electrostatic force) in bringing a charge
q from a point R to a point P is q(VP–VR), which is the difference in
potential energy of charge q between the final and initial points 2 Potential at a point is the work done per unit charge (by an external
agency) in bringing a charge from infinity to that point Potential at a
point is arbitrary to within an additive constant, since it is the potential
difference between two points which is physically significant |
1 | 2295-2298 | 2 Potential at a point is the work done per unit charge (by an external
agency) in bringing a charge from infinity to that point Potential at a
point is arbitrary to within an additive constant, since it is the potential
difference between two points which is physically significant If potential
at infinity is chosen to be zero; potential at a point with position vector
r due to a point charge Q placed at the origin is given is given by
1
( )
4
o
Q
V
r
ε
=
π
r
3 |
1 | 2296-2299 | Potential at a point is the work done per unit charge (by an external
agency) in bringing a charge from infinity to that point Potential at a
point is arbitrary to within an additive constant, since it is the potential
difference between two points which is physically significant If potential
at infinity is chosen to be zero; potential at a point with position vector
r due to a point charge Q placed at the origin is given is given by
1
( )
4
o
Q
V
r
ε
=
π
r
3 The electrostatic potential at a point with position vector r due to a
point dipole of dipole moment p placed at the origin is
ˆ2
1
( )
=4 ε
π
p |
1 | 2297-2300 | Potential at a
point is arbitrary to within an additive constant, since it is the potential
difference between two points which is physically significant If potential
at infinity is chosen to be zero; potential at a point with position vector
r due to a point charge Q placed at the origin is given is given by
1
( )
4
o
Q
V
r
ε
=
π
r
3 The electrostatic potential at a point with position vector r due to a
point dipole of dipole moment p placed at the origin is
ˆ2
1
( )
=4 ε
π
p r
r
o
V
r
The result is true also for a dipole (with charges –q and q separated by
2a) for r >> a |
1 | 2298-2301 | If potential
at infinity is chosen to be zero; potential at a point with position vector
r due to a point charge Q placed at the origin is given is given by
1
( )
4
o
Q
V
r
ε
=
π
r
3 The electrostatic potential at a point with position vector r due to a
point dipole of dipole moment p placed at the origin is
ˆ2
1
( )
=4 ε
π
p r
r
o
V
r
The result is true also for a dipole (with charges –q and q separated by
2a) for r >> a 4 |
1 | 2299-2302 | The electrostatic potential at a point with position vector r due to a
point dipole of dipole moment p placed at the origin is
ˆ2
1
( )
=4 ε
π
p r
r
o
V
r
The result is true also for a dipole (with charges –q and q separated by
2a) for r >> a 4 For a charge configuration q1, q2, |
1 | 2300-2303 | r
r
o
V
r
The result is true also for a dipole (with charges –q and q separated by
2a) for r >> a 4 For a charge configuration q1, q2, , qn with position vectors r1,
r2, |
1 | 2301-2304 | 4 For a charge configuration q1, q2, , qn with position vectors r1,
r2, rn, the potential at a point P is given by the superposition principle
1
2
0
1P
2P
P
1
( |
1 | 2302-2305 | For a charge configuration q1, q2, , qn with position vectors r1,
r2, rn, the potential at a point P is given by the superposition principle
1
2
0
1P
2P
P
1
( )
4
n
n
q
q
q
V
r
r
r
ε
=
+
+
+
π
where r1P is the distance between q1 and P, as and so on |
1 | 2303-2306 | , qn with position vectors r1,
r2, rn, the potential at a point P is given by the superposition principle
1
2
0
1P
2P
P
1
( )
4
n
n
q
q
q
V
r
r
r
ε
=
+
+
+
π
where r1P is the distance between q1 and P, as and so on 5 |
1 | 2304-2307 | rn, the potential at a point P is given by the superposition principle
1
2
0
1P
2P
P
1
( )
4
n
n
q
q
q
V
r
r
r
ε
=
+
+
+
π
where r1P is the distance between q1 and P, as and so on 5 An equipotential surface is a surface over which potential has a constant
value |
1 | 2305-2308 | )
4
n
n
q
q
q
V
r
r
r
ε
=
+
+
+
π
where r1P is the distance between q1 and P, as and so on 5 An equipotential surface is a surface over which potential has a constant
value For a point charge, concentric spheres centred at a location of the
charge are equipotential surfaces |
1 | 2306-2309 | 5 An equipotential surface is a surface over which potential has a constant
value For a point charge, concentric spheres centred at a location of the
charge are equipotential surfaces The electric field E at a point is
perpendicular to the equipotential surface through the point |
1 | 2307-2310 | An equipotential surface is a surface over which potential has a constant
value For a point charge, concentric spheres centred at a location of the
charge are equipotential surfaces The electric field E at a point is
perpendicular to the equipotential surface through the point E is in the
direction of the steepest decrease of potential |
1 | 2308-2311 | For a point charge, concentric spheres centred at a location of the
charge are equipotential surfaces The electric field E at a point is
perpendicular to the equipotential surface through the point E is in the
direction of the steepest decrease of potential Rationalised 2023-24
Electrostatic Potential
and Capacitance
77
6 |
1 | 2309-2312 | The electric field E at a point is
perpendicular to the equipotential surface through the point E is in the
direction of the steepest decrease of potential Rationalised 2023-24
Electrostatic Potential
and Capacitance
77
6 Potential energy stored in a system of charges is the work done (by an
external agency) in assembling the charges at their locations |
1 | 2310-2313 | E is in the
direction of the steepest decrease of potential Rationalised 2023-24
Electrostatic Potential
and Capacitance
77
6 Potential energy stored in a system of charges is the work done (by an
external agency) in assembling the charges at their locations Potential
energy of two charges q1, q2 at r1, r2 is given by
1
2
0
12
1
4
q q
U
r
ε
=
π
where r12 is distance between q1 and q2 |
1 | 2311-2314 | Rationalised 2023-24
Electrostatic Potential
and Capacitance
77
6 Potential energy stored in a system of charges is the work done (by an
external agency) in assembling the charges at their locations Potential
energy of two charges q1, q2 at r1, r2 is given by
1
2
0
12
1
4
q q
U
r
ε
=
π
where r12 is distance between q1 and q2 7 |
1 | 2312-2315 | Potential energy stored in a system of charges is the work done (by an
external agency) in assembling the charges at their locations Potential
energy of two charges q1, q2 at r1, r2 is given by
1
2
0
12
1
4
q q
U
r
ε
=
π
where r12 is distance between q1 and q2 7 The potential energy of a charge q in an external potential V(r) is qV(r) |
1 | 2313-2316 | Potential
energy of two charges q1, q2 at r1, r2 is given by
1
2
0
12
1
4
q q
U
r
ε
=
π
where r12 is distance between q1 and q2 7 The potential energy of a charge q in an external potential V(r) is qV(r) The potential energy of a dipole moment p in a uniform electric field E
is –p |
1 | 2314-2317 | 7 The potential energy of a charge q in an external potential V(r) is qV(r) The potential energy of a dipole moment p in a uniform electric field E
is –p E |
1 | 2315-2318 | The potential energy of a charge q in an external potential V(r) is qV(r) The potential energy of a dipole moment p in a uniform electric field E
is –p E 8 |
1 | 2316-2319 | The potential energy of a dipole moment p in a uniform electric field E
is –p E 8 Electrostatics field E is zero in the interior of a conductor; just outside
the surface of a charged conductor, E is normal to the surface given by
0
E=εσˆ
n where ˆn is the unit vector along the outward normal to the
surface and s is the surface charge density |
1 | 2317-2320 | E 8 Electrostatics field E is zero in the interior of a conductor; just outside
the surface of a charged conductor, E is normal to the surface given by
0
E=εσˆ
n where ˆn is the unit vector along the outward normal to the
surface and s is the surface charge density Charges in a conductor can
reside only at its surface |
1 | 2318-2321 | 8 Electrostatics field E is zero in the interior of a conductor; just outside
the surface of a charged conductor, E is normal to the surface given by
0
E=εσˆ
n where ˆn is the unit vector along the outward normal to the
surface and s is the surface charge density Charges in a conductor can
reside only at its surface Potential is constant within and on the surface
of a conductor |
1 | 2319-2322 | Electrostatics field E is zero in the interior of a conductor; just outside
the surface of a charged conductor, E is normal to the surface given by
0
E=εσˆ
n where ˆn is the unit vector along the outward normal to the
surface and s is the surface charge density Charges in a conductor can
reside only at its surface Potential is constant within and on the surface
of a conductor In a cavity within a conductor (with no charges), the
electric field is zero |
1 | 2320-2323 | Charges in a conductor can
reside only at its surface Potential is constant within and on the surface
of a conductor In a cavity within a conductor (with no charges), the
electric field is zero 9 |
1 | 2321-2324 | Potential is constant within and on the surface
of a conductor In a cavity within a conductor (with no charges), the
electric field is zero 9 A capacitor is a system of two conductors separated by an insulator |
1 | 2322-2325 | In a cavity within a conductor (with no charges), the
electric field is zero 9 A capacitor is a system of two conductors separated by an insulator Its
capacitance is defined by C = Q/V, where Q and –Q are the charges on the
two conductors and V is the potential difference between them |
1 | 2323-2326 | 9 A capacitor is a system of two conductors separated by an insulator Its
capacitance is defined by C = Q/V, where Q and –Q are the charges on the
two conductors and V is the potential difference between them C is
determined purely geometrically, by the shapes, sizes and relative
positions of the two conductors |
1 | 2324-2327 | A capacitor is a system of two conductors separated by an insulator Its
capacitance is defined by C = Q/V, where Q and –Q are the charges on the
two conductors and V is the potential difference between them C is
determined purely geometrically, by the shapes, sizes and relative
positions of the two conductors The unit of capacitance is farad:,
1 F = 1 C V –1 |
1 | 2325-2328 | Its
capacitance is defined by C = Q/V, where Q and –Q are the charges on the
two conductors and V is the potential difference between them C is
determined purely geometrically, by the shapes, sizes and relative
positions of the two conductors The unit of capacitance is farad:,
1 F = 1 C V –1 For a parallel plate capacitor (with vacuum between the
plates),
C =
0
dA
ε
where A is the area of each plate and d the separation between them |
1 | 2326-2329 | C is
determined purely geometrically, by the shapes, sizes and relative
positions of the two conductors The unit of capacitance is farad:,
1 F = 1 C V –1 For a parallel plate capacitor (with vacuum between the
plates),
C =
0
dA
ε
where A is the area of each plate and d the separation between them 10 |
1 | 2327-2330 | The unit of capacitance is farad:,
1 F = 1 C V –1 For a parallel plate capacitor (with vacuum between the
plates),
C =
0
dA
ε
where A is the area of each plate and d the separation between them 10 If the medium between the plates of a capacitor is filled with an insulating
substance (dielectric), the electric field due to the charged plates induces
a net dipole moment in the dielectric |
1 | 2328-2331 | For a parallel plate capacitor (with vacuum between the
plates),
C =
0
dA
ε
where A is the area of each plate and d the separation between them 10 If the medium between the plates of a capacitor is filled with an insulating
substance (dielectric), the electric field due to the charged plates induces
a net dipole moment in the dielectric This effect, called polarisation,
gives rise to a field in the opposite direction |
1 | 2329-2332 | 10 If the medium between the plates of a capacitor is filled with an insulating
substance (dielectric), the electric field due to the charged plates induces
a net dipole moment in the dielectric This effect, called polarisation,
gives rise to a field in the opposite direction The net electric field inside
the dielectric and hence the potential difference between the plates is
thus reduced |
1 | 2330-2333 | If the medium between the plates of a capacitor is filled with an insulating
substance (dielectric), the electric field due to the charged plates induces
a net dipole moment in the dielectric This effect, called polarisation,
gives rise to a field in the opposite direction The net electric field inside
the dielectric and hence the potential difference between the plates is
thus reduced Consequently, the capacitance C increases from its value
C0 when there is no medium (vacuum),
C = KC0
where K is the dielectric constant of the insulating substance |
1 | 2331-2334 | This effect, called polarisation,
gives rise to a field in the opposite direction The net electric field inside
the dielectric and hence the potential difference between the plates is
thus reduced Consequently, the capacitance C increases from its value
C0 when there is no medium (vacuum),
C = KC0
where K is the dielectric constant of the insulating substance 11 |
1 | 2332-2335 | The net electric field inside
the dielectric and hence the potential difference between the plates is
thus reduced Consequently, the capacitance C increases from its value
C0 when there is no medium (vacuum),
C = KC0
where K is the dielectric constant of the insulating substance 11 For capacitors in the series combination, the total capacitance C is given by
1
2
3
1
1
1
1 |
1 | 2333-2336 | Consequently, the capacitance C increases from its value
C0 when there is no medium (vacuum),
C = KC0
where K is the dielectric constant of the insulating substance 11 For capacitors in the series combination, the total capacitance C is given by
1
2
3
1
1
1
1 C
C
C
C
=
+
+
+
In the parallel combination, the total capacitance C is:
C = C1 + C2 + C3 + |
1 | 2334-2337 | 11 For capacitors in the series combination, the total capacitance C is given by
1
2
3
1
1
1
1 C
C
C
C
=
+
+
+
In the parallel combination, the total capacitance C is:
C = C1 + C2 + C3 + where C1, C2, C3 |
1 | 2335-2338 | For capacitors in the series combination, the total capacitance C is given by
1
2
3
1
1
1
1 C
C
C
C
=
+
+
+
In the parallel combination, the total capacitance C is:
C = C1 + C2 + C3 + where C1, C2, C3 are individual capacitances |
1 | 2336-2339 | C
C
C
C
=
+
+
+
In the parallel combination, the total capacitance C is:
C = C1 + C2 + C3 + where C1, C2, C3 are individual capacitances Rationalised 2023-24
Physics
78
12 |
1 | 2337-2340 | where C1, C2, C3 are individual capacitances Rationalised 2023-24
Physics
78
12 The energy U stored in a capacitor of capacitance C, with charge Q and
voltage V is
U
QV
CV
Q
C
=
=
=
21
21
1
2
2
2
The electric energy density (energy per unit volume) in a region with
electric field is (1/2)e0E2 |
1 | 2338-2341 | are individual capacitances Rationalised 2023-24
Physics
78
12 The energy U stored in a capacitor of capacitance C, with charge Q and
voltage V is
U
QV
CV
Q
C
=
=
=
21
21
1
2
2
2
The electric energy density (energy per unit volume) in a region with
electric field is (1/2)e0E2 Physical quantity
Symbol
Dimensions
Unit
Remark
Potential
or V
[M1 L2 T–3 A–1]
V
Potential difference is
physically significant
Capacitance
C
[M–1 L–2 T–4 A2]
F
Polarisation
P
[L–2 AT]
C m-2
Dipole moment per unit
volume
Dielectric constant
K
[Dimensionless]
POINTS TO PONDER
1 |
1 | 2339-2342 | Rationalised 2023-24
Physics
78
12 The energy U stored in a capacitor of capacitance C, with charge Q and
voltage V is
U
QV
CV
Q
C
=
=
=
21
21
1
2
2
2
The electric energy density (energy per unit volume) in a region with
electric field is (1/2)e0E2 Physical quantity
Symbol
Dimensions
Unit
Remark
Potential
or V
[M1 L2 T–3 A–1]
V
Potential difference is
physically significant
Capacitance
C
[M–1 L–2 T–4 A2]
F
Polarisation
P
[L–2 AT]
C m-2
Dipole moment per unit
volume
Dielectric constant
K
[Dimensionless]
POINTS TO PONDER
1 Electrostatics deals with forces between charges at rest |
1 | 2340-2343 | The energy U stored in a capacitor of capacitance C, with charge Q and
voltage V is
U
QV
CV
Q
C
=
=
=
21
21
1
2
2
2
The electric energy density (energy per unit volume) in a region with
electric field is (1/2)e0E2 Physical quantity
Symbol
Dimensions
Unit
Remark
Potential
or V
[M1 L2 T–3 A–1]
V
Potential difference is
physically significant
Capacitance
C
[M–1 L–2 T–4 A2]
F
Polarisation
P
[L–2 AT]
C m-2
Dipole moment per unit
volume
Dielectric constant
K
[Dimensionless]
POINTS TO PONDER
1 Electrostatics deals with forces between charges at rest But if there is a
force on a charge, how can it be at rest |
1 | 2341-2344 | Physical quantity
Symbol
Dimensions
Unit
Remark
Potential
or V
[M1 L2 T–3 A–1]
V
Potential difference is
physically significant
Capacitance
C
[M–1 L–2 T–4 A2]
F
Polarisation
P
[L–2 AT]
C m-2
Dipole moment per unit
volume
Dielectric constant
K
[Dimensionless]
POINTS TO PONDER
1 Electrostatics deals with forces between charges at rest But if there is a
force on a charge, how can it be at rest Thus, when we are talking of
electrostatic force between charges, it should be understood that each
charge is being kept at rest by some unspecified force that opposes the
net Coulomb force on the charge |
1 | 2342-2345 | Electrostatics deals with forces between charges at rest But if there is a
force on a charge, how can it be at rest Thus, when we are talking of
electrostatic force between charges, it should be understood that each
charge is being kept at rest by some unspecified force that opposes the
net Coulomb force on the charge 2 |
1 | 2343-2346 | But if there is a
force on a charge, how can it be at rest Thus, when we are talking of
electrostatic force between charges, it should be understood that each
charge is being kept at rest by some unspecified force that opposes the
net Coulomb force on the charge 2 A capacitor is so configured that it confines the electric field lines within
a small region of space |
1 | 2344-2347 | Thus, when we are talking of
electrostatic force between charges, it should be understood that each
charge is being kept at rest by some unspecified force that opposes the
net Coulomb force on the charge 2 A capacitor is so configured that it confines the electric field lines within
a small region of space Thus, even though field may have considerable
strength, the potential difference between the two conductors of a
capacitor is small |
1 | 2345-2348 | 2 A capacitor is so configured that it confines the electric field lines within
a small region of space Thus, even though field may have considerable
strength, the potential difference between the two conductors of a
capacitor is small 3 |
1 | 2346-2349 | A capacitor is so configured that it confines the electric field lines within
a small region of space Thus, even though field may have considerable
strength, the potential difference between the two conductors of a
capacitor is small 3 Electric field is discontinuous across the surface of a spherical charged
shell |
1 | 2347-2350 | Thus, even though field may have considerable
strength, the potential difference between the two conductors of a
capacitor is small 3 Electric field is discontinuous across the surface of a spherical charged
shell It is zero inside and σε0 ˆn outside |
1 | 2348-2351 | 3 Electric field is discontinuous across the surface of a spherical charged
shell It is zero inside and σε0 ˆn outside Electric potential is, however
continuous across the surface, equal to q/4pe0R at the surface |
1 | 2349-2352 | Electric field is discontinuous across the surface of a spherical charged
shell It is zero inside and σε0 ˆn outside Electric potential is, however
continuous across the surface, equal to q/4pe0R at the surface 4 |
1 | 2350-2353 | It is zero inside and σε0 ˆn outside Electric potential is, however
continuous across the surface, equal to q/4pe0R at the surface 4 The torque p × E on a dipole causes it to oscillate about E |
1 | 2351-2354 | Electric potential is, however
continuous across the surface, equal to q/4pe0R at the surface 4 The torque p × E on a dipole causes it to oscillate about E Only if there
is a dissipative mechanism, the oscillations are damped and the dipole
eventually aligns with E |
1 | 2352-2355 | 4 The torque p × E on a dipole causes it to oscillate about E Only if there
is a dissipative mechanism, the oscillations are damped and the dipole
eventually aligns with E 5 |
1 | 2353-2356 | The torque p × E on a dipole causes it to oscillate about E Only if there
is a dissipative mechanism, the oscillations are damped and the dipole
eventually aligns with E 5 Potential due to a charge q at its own location is not defined – it is
infinite |
1 | 2354-2357 | Only if there
is a dissipative mechanism, the oscillations are damped and the dipole
eventually aligns with E 5 Potential due to a charge q at its own location is not defined – it is
infinite 6 |
1 | 2355-2358 | 5 Potential due to a charge q at its own location is not defined – it is
infinite 6 In the expression qV (r) for potential energy of a charge q, V (r) is the
potential due to external charges and not the potential due to q |
1 | 2356-2359 | Potential due to a charge q at its own location is not defined – it is
infinite 6 In the expression qV (r) for potential energy of a charge q, V (r) is the
potential due to external charges and not the potential due to q As seen
in point 5, this expression will be ill-defined if V (r) includes potential
due to a charge q itself |
1 | 2357-2360 | 6 In the expression qV (r) for potential energy of a charge q, V (r) is the
potential due to external charges and not the potential due to q As seen
in point 5, this expression will be ill-defined if V (r) includes potential
due to a charge q itself Rationalised 2023-24
Electrostatic Potential
and Capacitance
79
7 |
1 | 2358-2361 | In the expression qV (r) for potential energy of a charge q, V (r) is the
potential due to external charges and not the potential due to q As seen
in point 5, this expression will be ill-defined if V (r) includes potential
due to a charge q itself Rationalised 2023-24
Electrostatic Potential
and Capacitance
79
7 A cavity inside a conductor is shielded from outside electrical influences |
1 | 2359-2362 | As seen
in point 5, this expression will be ill-defined if V (r) includes potential
due to a charge q itself Rationalised 2023-24
Electrostatic Potential
and Capacitance
79
7 A cavity inside a conductor is shielded from outside electrical influences It is worth noting that electrostatic shielding does not work the other
way round; that is, if you put charges inside the cavity, the exterior of
the conductor is not shielded from the fields by the inside charges |
1 | 2360-2363 | Rationalised 2023-24
Electrostatic Potential
and Capacitance
79
7 A cavity inside a conductor is shielded from outside electrical influences It is worth noting that electrostatic shielding does not work the other
way round; that is, if you put charges inside the cavity, the exterior of
the conductor is not shielded from the fields by the inside charges EXERCISES
2 |
1 | 2361-2364 | A cavity inside a conductor is shielded from outside electrical influences It is worth noting that electrostatic shielding does not work the other
way round; that is, if you put charges inside the cavity, the exterior of
the conductor is not shielded from the fields by the inside charges EXERCISES
2 1
Two charges 5 × 10–8 C and –3 × 10–8 C are located 16 cm apart |
1 | 2362-2365 | It is worth noting that electrostatic shielding does not work the other
way round; that is, if you put charges inside the cavity, the exterior of
the conductor is not shielded from the fields by the inside charges EXERCISES
2 1
Two charges 5 × 10–8 C and –3 × 10–8 C are located 16 cm apart At
what point(s) on the line joining the two charges is the electric
potential zero |
1 | 2363-2366 | EXERCISES
2 1
Two charges 5 × 10–8 C and –3 × 10–8 C are located 16 cm apart At
what point(s) on the line joining the two charges is the electric
potential zero Take the potential at infinity to be zero |
1 | 2364-2367 | 1
Two charges 5 × 10–8 C and –3 × 10–8 C are located 16 cm apart At
what point(s) on the line joining the two charges is the electric
potential zero Take the potential at infinity to be zero 2 |
1 | 2365-2368 | At
what point(s) on the line joining the two charges is the electric
potential zero Take the potential at infinity to be zero 2 2
A regular hexagon of side 10 cm has a charge 5 mC at each of its
vertices |
1 | 2366-2369 | Take the potential at infinity to be zero 2 2
A regular hexagon of side 10 cm has a charge 5 mC at each of its
vertices Calculate the potential at the centre of the hexagon |
1 | 2367-2370 | 2 2
A regular hexagon of side 10 cm has a charge 5 mC at each of its
vertices Calculate the potential at the centre of the hexagon 2 |
1 | 2368-2371 | 2
A regular hexagon of side 10 cm has a charge 5 mC at each of its
vertices Calculate the potential at the centre of the hexagon 2 3
Two charges 2 mC and –2 mC are placed at points A and B 6 cm
apart |
1 | 2369-2372 | Calculate the potential at the centre of the hexagon 2 3
Two charges 2 mC and –2 mC are placed at points A and B 6 cm
apart (a)
Identify an equipotential surface of the system |
1 | 2370-2373 | 2 3
Two charges 2 mC and –2 mC are placed at points A and B 6 cm
apart (a)
Identify an equipotential surface of the system (b)
What is the direction of the electric field at every point on this
surface |
1 | 2371-2374 | 3
Two charges 2 mC and –2 mC are placed at points A and B 6 cm
apart (a)
Identify an equipotential surface of the system (b)
What is the direction of the electric field at every point on this
surface 2 |
1 | 2372-2375 | (a)
Identify an equipotential surface of the system (b)
What is the direction of the electric field at every point on this
surface 2 4
A spherical conductor of radius 12 cm has a charge of 1 |
1 | 2373-2376 | (b)
What is the direction of the electric field at every point on this
surface 2 4
A spherical conductor of radius 12 cm has a charge of 1 6 × 10–7C
distributed uniformly on its surface |
1 | 2374-2377 | 2 4
A spherical conductor of radius 12 cm has a charge of 1 6 × 10–7C
distributed uniformly on its surface What is the electric field
(a)
inside the sphere
(b)
just outside the sphere
(c)
at a point 18 cm from the centre of the sphere |
1 | 2375-2378 | 4
A spherical conductor of radius 12 cm has a charge of 1 6 × 10–7C
distributed uniformly on its surface What is the electric field
(a)
inside the sphere
(b)
just outside the sphere
(c)
at a point 18 cm from the centre of the sphere 2 |
1 | 2376-2379 | 6 × 10–7C
distributed uniformly on its surface What is the electric field
(a)
inside the sphere
(b)
just outside the sphere
(c)
at a point 18 cm from the centre of the sphere 2 5
A parallel plate capacitor with air between the plates has a
capacitance of 8 pF (1pF = 10–12 F) |
1 | 2377-2380 | What is the electric field
(a)
inside the sphere
(b)
just outside the sphere
(c)
at a point 18 cm from the centre of the sphere 2 5
A parallel plate capacitor with air between the plates has a
capacitance of 8 pF (1pF = 10–12 F) What will be the capacitance if
the distance between the plates is reduced by half, and the space
between them is filled with a substance of dielectric constant 6 |
1 | 2378-2381 | 2 5
A parallel plate capacitor with air between the plates has a
capacitance of 8 pF (1pF = 10–12 F) What will be the capacitance if
the distance between the plates is reduced by half, and the space
between them is filled with a substance of dielectric constant 6 2 |
1 | 2379-2382 | 5
A parallel plate capacitor with air between the plates has a
capacitance of 8 pF (1pF = 10–12 F) What will be the capacitance if
the distance between the plates is reduced by half, and the space
between them is filled with a substance of dielectric constant 6 2 6
Three capacitors each of capacitance 9 pF are connected in series |
1 | 2380-2383 | What will be the capacitance if
the distance between the plates is reduced by half, and the space
between them is filled with a substance of dielectric constant 6 2 6
Three capacitors each of capacitance 9 pF are connected in series (a)
What is the total capacitance of the combination |
1 | 2381-2384 | 2 6
Three capacitors each of capacitance 9 pF are connected in series (a)
What is the total capacitance of the combination (b)
What is the potential difference across each capacitor if the
combination is connected to a 120 V supply |
1 | 2382-2385 | 6
Three capacitors each of capacitance 9 pF are connected in series (a)
What is the total capacitance of the combination (b)
What is the potential difference across each capacitor if the
combination is connected to a 120 V supply 2 |
1 | 2383-2386 | (a)
What is the total capacitance of the combination (b)
What is the potential difference across each capacitor if the
combination is connected to a 120 V supply 2 7
Three capacitors of capacitances 2 pF, 3 pF and 4 pF are connected
in parallel |
1 | 2384-2387 | (b)
What is the potential difference across each capacitor if the
combination is connected to a 120 V supply 2 7
Three capacitors of capacitances 2 pF, 3 pF and 4 pF are connected
in parallel (a)
What is the total capacitance of the combination |
1 | 2385-2388 | 2 7
Three capacitors of capacitances 2 pF, 3 pF and 4 pF are connected
in parallel (a)
What is the total capacitance of the combination (b)
Determine the charge on each capacitor if the combination is
connected to a 100 V supply |
1 | 2386-2389 | 7
Three capacitors of capacitances 2 pF, 3 pF and 4 pF are connected
in parallel (a)
What is the total capacitance of the combination (b)
Determine the charge on each capacitor if the combination is
connected to a 100 V supply 2 |
1 | 2387-2390 | (a)
What is the total capacitance of the combination (b)
Determine the charge on each capacitor if the combination is
connected to a 100 V supply 2 8
In a parallel plate capacitor with air between the plates, each plate
has an area of 6 × 10–3 m2 and the distance between the plates is 3 mm |
1 | 2388-2391 | (b)
Determine the charge on each capacitor if the combination is
connected to a 100 V supply 2 8
In a parallel plate capacitor with air between the plates, each plate
has an area of 6 × 10–3 m2 and the distance between the plates is 3 mm Calculate the capacitance of the capacitor |
1 | 2389-2392 | 2 8
In a parallel plate capacitor with air between the plates, each plate
has an area of 6 × 10–3 m2 and the distance between the plates is 3 mm Calculate the capacitance of the capacitor If this capacitor is
connected to a 100 V supply, what is the charge on each plate of the
capacitor |
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