Electrostatic Potential
and Capacitance
Single Correct Type Question Which of the following statement(s) is(are) correct?
1. Which of the following graph correctly represents the 3
variation of electric potential (V) of a charged spherical (a) If rB = , then the electric field is zero everywhere
conductor of radius (R) with radial distance (r) from the 2
centre? [31 Jan 2023 (Shift-I)] outside B
V V (b) If rB = 3 , then the electric potential just outside B is
k 2
(a) (b)
∈0
0 R r 0 R r (c) If rB = 2, then the total charge of the configuration is
15πk
V V
5
(d) If rB = , then the magnitude of the electric field just
(c) (d) 2
13πk
outside B is
0 R r 0 R r ∈0
3. A charge Q is distributed over two concentric conducting
2. In the figure, the inner (shaded) region A represents a thin spherical shells radii r and R (R > r). If the surface
sphere of radius rA=1, within which the electrostatic charge densities on the two shells are equal, the electric
charge density varies with the radial distance r from the potential at the common center is
center as ρA= kr, where k is positive. In the spherical [2 Sep, 2020 (Shift-II)]
shell B of outer radius rB, the electrostatic charge density
2k
varies as ρ B = . Assume that dimensions are taken
r
care of. All physical quantities are in their SI units. r
[JEE Adv, 2022] R
rA 1 (R + r) 1 ( R + 2r )Q
(a) Q (b)
A 4πε0 ( R 2 + r 2 ) 4πε0 2( R 2 + r 2 )
1 (R + r) 1 (2 R + r )
(c) Q (d) Q
B 4πε0 2( R 2 + r 2 ) 4πε0 ( R 2 + r 2 )
rB
1 JEE PYQs Physics
, 4. A system of three charges are placed as shown in the figure 10q 10q
If D >> d,the potential energy of the system is best given (a) V = 0; E = 0 (b) V =
= ;E
4πε0 R 4πε0 R 2
by [9 April, 2019 (Shift-I)]
10q 10q
(c) V = =E=0 (d) V = 0; E =
4πε0 R 4πε0 R 2
8. The electric field in a region is given by=
E ( Ax + B ) iˆ,
Q where E is in NC and x is in metres. The values of constants
–1
are A = 20 SI unit and B = 10 SI unit. If the potential at
1 q 2
qQd 1 q 2
qQd x = 1 is V1 and that at x = – 5 is V2, then V1 – V2 is:
(a) − − 2 (b) + + 2
4πε0 d D 4πε0 d D [8 April, 2019 (Shift-II)]
(a) 180 V (b) –520 V (c) 320 V (d) –48 V
1 q 2 2qQd 1 q 2 qQd 9. An electric dipole is formed by two charges + q and – q
(c) − + (d) − −
4πε0 d D2 4πε0 d 2 D 2 located in xy - plane at (0, 2) mm and (0, –2) mm, respectively,
as shown in the figure. The electric potential at point P(100,
100) mm due to the dipole is V0. The charges + q and – q
5. The given graph shows variation (with distance r from are then moved to the points (–1, 2) mm and (1, –2) mm,
center) of [11 Jan, 2019 (Shift-I)] respectively. What is the value of electric potential at P due
to the new dipole ? [JEE Adv, 2023]
y
r0 P(100, 100) mm
≈
≈
r0 r +q (0, 2) mm
(–1, 2) mm
(a) Potential of a uniformly charged spherical shell x
O
≈
(b) Electric field of a uniformly charged sphere –q (1, –2) mm
(c) Electric field of uniformly charged spherical shell (0, –2) mm
(a) V0 /4 (b) V0 /2
(d) Potential of a uniformly charged sphere
(c) V (d) 3V0/4
6. Consider two charged metallic spheres S1 and S2 of radii
R1 and R2, respectively. The electric fields E1 (on S1) and 10. A point dipole p = − p0 x̂ is kept at the origin. The
E2 (on S2) on their surfaces are such that E1/E2 = R1/R2. potential and electric field due to this dipole on the y-axis
Then the ratio V1(on S1) / V2 (on S2) of the electrostatic at a distance d are, respectively
(Take V = 0 at infinity) [12 April, 2019 (Shift-I)]
potentials on each sphere is [8 Jan, 2020 (Shift-II)]
p p p −p
2 3 (a) , (b) ,
R R R1 4πε0 d 2 4πε0 d 3 4πε0 d 2 4πε0 d 3
(a) R1 (b) 1 (c) 2 (d)
R2 R2 R1 R2
−p
p
(c) 0, (d) 0,
7. Ten charges are placed on the circumference of a circle 4πε0 d 3 4πε0 d 3
of radius R with constant angular separation between 11. A parallel plate capacitor has plate area 40 cm2 and plate
successive charges. Alternate charges 1, 3, 5, 7, 9 have separation 2 mm. The space between the plates is filled
with a dielectric medium of thickness 1 mm and dielectric
charge (+q) each, while 2, 4, 6, 8, 10 have charge (–q)
constant 5. The new capacitance of the system is :
each. The potential V and the electric field E at the center [25 Jan, 2023 (Shift-I)]
of the circle are respectively. (Take V = 0 at infinity) 3 10
[5 Sep, 2020 (Shift-II)] (a) 24ε0 F (b) ε0 F (c) ε0 F (d) 10ε0 F
10 3
2 JEE PYQs Physics
and Capacitance
Single Correct Type Question Which of the following statement(s) is(are) correct?
1. Which of the following graph correctly represents the 3
variation of electric potential (V) of a charged spherical (a) If rB = , then the electric field is zero everywhere
conductor of radius (R) with radial distance (r) from the 2
centre? [31 Jan 2023 (Shift-I)] outside B
V V (b) If rB = 3 , then the electric potential just outside B is
k 2
(a) (b)
∈0
0 R r 0 R r (c) If rB = 2, then the total charge of the configuration is
15πk
V V
5
(d) If rB = , then the magnitude of the electric field just
(c) (d) 2
13πk
outside B is
0 R r 0 R r ∈0
3. A charge Q is distributed over two concentric conducting
2. In the figure, the inner (shaded) region A represents a thin spherical shells radii r and R (R > r). If the surface
sphere of radius rA=1, within which the electrostatic charge densities on the two shells are equal, the electric
charge density varies with the radial distance r from the potential at the common center is
center as ρA= kr, where k is positive. In the spherical [2 Sep, 2020 (Shift-II)]
shell B of outer radius rB, the electrostatic charge density
2k
varies as ρ B = . Assume that dimensions are taken
r
care of. All physical quantities are in their SI units. r
[JEE Adv, 2022] R
rA 1 (R + r) 1 ( R + 2r )Q
(a) Q (b)
A 4πε0 ( R 2 + r 2 ) 4πε0 2( R 2 + r 2 )
1 (R + r) 1 (2 R + r )
(c) Q (d) Q
B 4πε0 2( R 2 + r 2 ) 4πε0 ( R 2 + r 2 )
rB
1 JEE PYQs Physics
, 4. A system of three charges are placed as shown in the figure 10q 10q
If D >> d,the potential energy of the system is best given (a) V = 0; E = 0 (b) V =
= ;E
4πε0 R 4πε0 R 2
by [9 April, 2019 (Shift-I)]
10q 10q
(c) V = =E=0 (d) V = 0; E =
4πε0 R 4πε0 R 2
8. The electric field in a region is given by=
E ( Ax + B ) iˆ,
Q where E is in NC and x is in metres. The values of constants
–1
are A = 20 SI unit and B = 10 SI unit. If the potential at
1 q 2
qQd 1 q 2
qQd x = 1 is V1 and that at x = – 5 is V2, then V1 – V2 is:
(a) − − 2 (b) + + 2
4πε0 d D 4πε0 d D [8 April, 2019 (Shift-II)]
(a) 180 V (b) –520 V (c) 320 V (d) –48 V
1 q 2 2qQd 1 q 2 qQd 9. An electric dipole is formed by two charges + q and – q
(c) − + (d) − −
4πε0 d D2 4πε0 d 2 D 2 located in xy - plane at (0, 2) mm and (0, –2) mm, respectively,
as shown in the figure. The electric potential at point P(100,
100) mm due to the dipole is V0. The charges + q and – q
5. The given graph shows variation (with distance r from are then moved to the points (–1, 2) mm and (1, –2) mm,
center) of [11 Jan, 2019 (Shift-I)] respectively. What is the value of electric potential at P due
to the new dipole ? [JEE Adv, 2023]
y
r0 P(100, 100) mm
≈
≈
r0 r +q (0, 2) mm
(–1, 2) mm
(a) Potential of a uniformly charged spherical shell x
O
≈
(b) Electric field of a uniformly charged sphere –q (1, –2) mm
(c) Electric field of uniformly charged spherical shell (0, –2) mm
(a) V0 /4 (b) V0 /2
(d) Potential of a uniformly charged sphere
(c) V (d) 3V0/4
6. Consider two charged metallic spheres S1 and S2 of radii
R1 and R2, respectively. The electric fields E1 (on S1) and 10. A point dipole p = − p0 x̂ is kept at the origin. The
E2 (on S2) on their surfaces are such that E1/E2 = R1/R2. potential and electric field due to this dipole on the y-axis
Then the ratio V1(on S1) / V2 (on S2) of the electrostatic at a distance d are, respectively
(Take V = 0 at infinity) [12 April, 2019 (Shift-I)]
potentials on each sphere is [8 Jan, 2020 (Shift-II)]
p p p −p
2 3 (a) , (b) ,
R R R1 4πε0 d 2 4πε0 d 3 4πε0 d 2 4πε0 d 3
(a) R1 (b) 1 (c) 2 (d)
R2 R2 R1 R2
−p
p
(c) 0, (d) 0,
7. Ten charges are placed on the circumference of a circle 4πε0 d 3 4πε0 d 3
of radius R with constant angular separation between 11. A parallel plate capacitor has plate area 40 cm2 and plate
successive charges. Alternate charges 1, 3, 5, 7, 9 have separation 2 mm. The space between the plates is filled
with a dielectric medium of thickness 1 mm and dielectric
charge (+q) each, while 2, 4, 6, 8, 10 have charge (–q)
constant 5. The new capacitance of the system is :
each. The potential V and the electric field E at the center [25 Jan, 2023 (Shift-I)]
of the circle are respectively. (Take V = 0 at infinity) 3 10
[5 Sep, 2020 (Shift-II)] (a) 24ε0 F (b) ε0 F (c) ε0 F (d) 10ε0 F
10 3
2 JEE PYQs Physics
