Electric Potential and Capacitance | Physics JEE previous year questions with Solutions

Q 1 :
Two charged conducting spheres of radii a and b are connected to each other by a conducting wire. The ratio of charges of the two spheres respectively is [2024]

$\frac{b}{a}$
$\sqrt{a b}$
$a b$
$\frac{a}{b}$

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(4)

$V_{a} = V_{b}$

$\frac{K Q_{a}}{a} = \frac{K Q_{b}}{b} \Rightarrow \frac{Q_{a}}{Q_{b}} = \frac{a}{b}$

Q 2 :
An electric charge $10^{- 6} μ C$ is placed at origin (0, 0) m of X-Y co-ordinate system. Two points P and Q are situated at $(\sqrt{3}, \sqrt{3}) m$ and $(\sqrt{6}, 0) m$ respectively. The potential difference between the points P and Q will be [2024]

$\sqrt{3} V$
$\sqrt{6} V$
$0 V$
$3 V$

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4

(3)

Potential difference $= \frac{K Q}{r_{1}} - \frac{K Q}{r_{2}}$

$r_{1} = \sqrt{{(\sqrt{3})}^{2} + {(\sqrt{3})}^{2}}$

$r_{2} = \sqrt{{(\sqrt{6})}^{2} + 0}$

As $r_{1} = r_{2} = \sqrt{6} m$

So potential difference = 0.

Q 3 :
Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A): Work done by electric field on moving a positive charge on an equipotential surface is always zero.

Reason (R): Electric lines of forces are always perpendicular to equipotential surfaces.

In the light of the above statements, choose the most appropriate answer from the given below: [2024]

Both (A) and (R) are correct but (R) is not the correct explanation of (A)
(A) is correct but (R) is not correct
(A) is not correct but (R) is correct
Both (A) and (R) are correct and (R) is the correct explanation of (A)

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(4)

Electric line of force are always perpendicular to equipotential surface so angle between force and displacement will always be $90^{o}$ . So work done is equal to 0.

Q 4 :
At the centre of a half ring of radius R = 10 cm and linear charge density 4 n $C m^{- 1}$ , the potential is $x π$ $V$ . The value of $x$ is _______ . [2024]

0%

(36) Potential at centre of half ring

$V = \frac{K Q}{R} = \frac{K λ π R}{R}$

$V = K λ π \Rightarrow V = 9 \times 10^{9} \times 4 \times 10^{- 9} π$

$\Rightarrow$ $V = 36 π V$

Q 5 :
The electric potential at the surface of an atomic nucleus $(z = 50)$ of radius $9 \times 10^{- 13}$ cm is ______ $\times 10^{6}$ V [2024]

0%

(8) Potential = $\frac{k Q}{R} = \frac{k . Z e}{R}$

$= \frac{9 \times 10^{9} \times 50 \times 1.6 \times 10^{- 19}}{9 \times 10^{- 13} \times 10^{- 2}} = 8 \times 10^{6} V$

Q 6 :
Three infinitely long wires with linear charge density $λ$ are placed along the x-axis, y-axis and z-axis respectively. Which of the following denotes an equipotential surface? [2025]

xy + yz + zx = constant
(x + y)(y + z)(z + x) = constant
$(x^{2} + y^{2}) (y^{2} + z^{2}) (z^{2} + x^{2})$ = constant
xyz = constant

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(3)

$V = - \int \vec{E} \cdot d \vec{r} = \int \frac{2 k λ}{r} d r = 2 k λ \ln r + c$

Net potential due to all wires

$V = 2 k λ \ln \sqrt{x^{2} + y^{2}} + 2 k λ \ln \sqrt{y^{2} + z^{2}} + 2 k λ \ln \sqrt{z^{2} + x^{2}} + c$

for V to be constant

$\sqrt{(x^{2} + y^{2}) (y^{2} + z^{2}) (z^{2} + x^{2})} = c'$

$∴ (x^{2} + y^{2}) (y^{2} + z^{2}) (z^{2} + x^{2}) = c$

where c = constant

Q 7 :
Two large plane parallel conducting plates are kept 10 cm apart as shown in figure. The potential difference between them is V. The potential difference between the points A and B (shown in the figure) is: [2025]

$\frac{1}{4} V$
$\frac{2}{5} V$
$\frac{3}{4} V$
1 V

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(2)

Using $△ V = E (△ d)$

V = E(10)

$V_{A B} = E . 4 = \frac{V}{10} \times 4 = \frac{2 V}{5}$

Q 8 :
The electrostatic potential on the surface of uniformly charged spherical shell of radius R = 10 cm is 120 V. The potential at the centre of shell, at a distance r = 5 cm from centre, and at a distance r = 15 cm from the centre of the shell respectively, are: [2025]

120 V, 120 V, 80 V
40 V, 40 V, 80 V
0 V, 0 V, 80 V
0 V, 120 V, 40 V

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(1)

Potential inside shell is equal to potential on surface

$V_{in} = V_{surface} = \frac{k Q}{R} = 120 V$

at r = 15 cm

$V = \frac{k Q}{r} = \frac{120 \times 10}{15} = 80 V$

Q 9 :
Two metal spheres of radius R and 3R have same surface charge density $σ$ . If they are brought in contact and then separated, the surface charge density on smaller and bigger sphere becomes $σ_{1}$ and $σ_{2}$ , respectively. The ratio $\frac{σ_{1}}{σ_{2}}$ is. [2025]

$\frac{1}{9}$
9
$\frac{1}{3}$
3

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(4)

For conducting sphere, $V = \frac{σ r}{ε_{0}}$

After contact, $V_{1} = V_{2}$

$σ_{1} r_{1} = σ_{2} r_{2} \Rightarrow \frac{σ_{1}}{σ_{2}} = \frac{r_{2}}{r_{1}} = 3$

Topic Question Set

Q 1 :
Two charged conducting spheres of radii a and b are connected to each other by a conducting wire. The ratio of charges of the two spheres respectively is [2024]

Q 2 :
An electric charge $10^{- 6} μ C$ is placed at origin (0, 0) m of X-Y co-ordinate system. Two points P and Q are situated at $(\sqrt{3}, \sqrt{3}) m$ and $(\sqrt{6}, 0) m$ respectively. The potential difference between the points P and Q will be [2024]

Q 4 :
At the centre of a half ring of radius R = 10 cm and linear charge density 4 n $C m^{- 1}$ , the potential is $x π$ $V$ . The value of $x$ is _______ . [2024]

0%

Q 5 :
The electric potential at the surface of an atomic nucleus $(z = 50)$ of radius $9 \times 10^{- 13}$ cm is ______ $\times 10^{6}$ V [2024]

0%

Q 6 :
Three infinitely long wires with linear charge density $λ$ are placed along the x-axis, y-axis and z-axis respectively. Which of the following denotes an equipotential surface? [2025]

Q 7 :
Two large plane parallel conducting plates are kept 10 cm apart as shown in figure. The potential difference between them is V. The potential difference between the points A and B (shown in the figure) is: [2025]

Q 8 :
The electrostatic potential on the surface of uniformly charged spherical shell of radius R = 10 cm is 120 V. The potential at the centre of shell, at a distance r = 5 cm from centre, and at a distance r = 15 cm from the centre of the shell respectively, are: [2025]

Q 9 :
Two metal spheres of radius R and 3R have same surface charge density $σ$ . If they are brought in contact and then separated, the surface charge density on smaller and bigger sphere becomes $σ_{1}$ and $σ_{2}$ , respectively. The ratio $\frac{σ_{1}}{σ_{2}}$ is. [2025]

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Topic Question Set

Q 1 : Two charged conducting spheres of radii a and b are connected to each other by a conducting wire. The ratio of charges of the two spheres respectively is [2024]

Q 2 : An electric charge 10-6μC is placed at origin (0, 0) m of X-Y co-ordinate system. Two points P and Q are situated at (3,3)m and (6,0)m respectively. The potential difference between the points P and Q will be [2024]

Q 4 : At the centre of a half ring of radius R = 10 cm and linear charge density 4 n Cm-1, the potential is xπ V. The value of x is _______ . [2024]

0%

Q 5 : The electric potential at the surface of an atomic nucleus (z=50) of radius 9×10-13 cm is ______ ×106V [2024]

0%

Q 6 : Three infinitely long wires with linear charge density λ are placed along the x-axis, y-axis and z-axis respectively. Which of the following denotes an equipotential surface? [2025]

Q 7 : Two large plane parallel conducting plates are kept 10 cm apart as shown in figure. The potential difference between them is V. The potential difference between the points A and B (shown in the figure) is: [2025]

Q 8 : The electrostatic potential on the surface of uniformly charged spherical shell of radius R = 10 cm is 120 V. The potential at the centre of shell, at a distance r = 5 cm from centre, and at a distance r = 15 cm from the centre of the shell respectively, are: [2025]

Q 9 : Two metal spheres of radius R and 3R have same surface charge density σ. If they are brought in contact and then separated, the surface charge density on smaller and bigger sphere becomes σ1 and σ2, respectively. The ratio σ1σ2 is. [2025]

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Q 1 :
Two charged conducting spheres of radii a and b are connected to each other by a conducting wire. The ratio of charges of the two spheres respectively is [2024]

Q 2 :
An electric charge $10^{- 6} μ C$ is placed at origin (0, 0) m of X-Y co-ordinate system. Two points P and Q are situated at $(\sqrt{3}, \sqrt{3}) m$ and $(\sqrt{6}, 0) m$ respectively. The potential difference between the points P and Q will be [2024]

Q 4 :
At the centre of a half ring of radius R = 10 cm and linear charge density 4 n $C m^{- 1}$ , the potential is $x π$ $V$ . The value of $x$ is _______ . [2024]

Q 5 :
The electric potential at the surface of an atomic nucleus $(z = 50)$ of radius $9 \times 10^{- 13}$ cm is ______ $\times 10^{6}$ V [2024]

Q 6 :
Three infinitely long wires with linear charge density $λ$ are placed along the x-axis, y-axis and z-axis respectively. Which of the following denotes an equipotential surface? [2025]

Q 7 :
Two large plane parallel conducting plates are kept 10 cm apart as shown in figure. The potential difference between them is V. The potential difference between the points A and B (shown in the figure) is: [2025]

Q 8 :
The electrostatic potential on the surface of uniformly charged spherical shell of radius R = 10 cm is 120 V. The potential at the centre of shell, at a distance r = 5 cm from centre, and at a distance r = 15 cm from the centre of the shell respectively, are: [2025]

Q 9 :
Two metal spheres of radius R and 3R have same surface charge density $σ$ . If they are brought in contact and then separated, the surface charge density on smaller and bigger sphere becomes $σ_{1}$ and $σ_{2}$ , respectively. The ratio $\frac{σ_{1}}{σ_{2}}$ is. [2025]