Electric Potential and Capacitance

25 JEE Main questions · Physics

Capacitance

PhysicsJEE Main 21 Jan 2026, Shift 1·Q9·MCQ·Easy–moderate
Open
A parallel plate capacitor has capacitance $C$ , when there is vacuum within the parallel plates. A sheet having thickness $\left(\frac13\right)^{\text{rd}}$ of the separation between the plates and relative permittivity $K$ is introduced between the plates. The new capacitance of the system is:
1. (1) $\dfrac{3KC}{2K+1}$
2. (2) $\dfrac{CK}{2+K}$
3. (3) $\dfrac{3CK^2}{(2K+1)^2}$
4. (4) $\dfrac{4KC}{3K-1}$
PhysicsJEE Main 22 Jan 2026, Shift 2·Q23·Numerical·Easy–moderate
Open
A capacitor $P$ with capacitance $10\times10^{-6}$ F is fully charged with a potential difference of 6.0 V and disconnected from the battery. The charged capacitor $P$ is connected across another capacitor $Q$ with capacitance $20\times10^{-6}$ F. The charge on capacitor $Q$ when equilibrium is established will be $\alpha\times10^{-5}$ C (assume capacitor $Q$ does not have any charge initially), the value of $\alpha$ is .
PhysicsJEE Main 23 Jan 2026, Shift 1·Q25·Numerical·Moderate
Open
The space between the plates of a parallel-plate capacitor of capacitance C (without any dielectric) is now filled with three dielectric slabs of dielectric constants $K_1 = 2$ , $K_2 = 3$ , and $K_3 = 5$ (as shown in the figure). If new capacitance is $\dfrac{n}{3}C$ then the value of n is .
PhysicsJEE Main 23 Jan 2026, Shift 2·Q9·MCQ·Easy–moderate
Open
A parallel plate capacitor with plate separation 5 mm is charged by a battery. On introducing a mica sheet of 2 mm and maintaining the connections of the plates with the terminals of the battery, it is found that it draws 25% more charge from the battery. The dielectric constant of mica is .
1. (1)2.5
2. (2)2.0
3. (3)1.5
4. (4)1.0
PhysicsJEE Main 24 Jan 2026, Shift 2·Q10·MCQ·Moderate
Open
Three parallel plate capacitors each with area $A$ and separation $d$ are filled with two dielectrics ( $k_1$ and $k_2$ ) in the following fashion. Which of the following is true? ( $k_1 > k_2$ )
1. (1) $C_B > C_C > C_A$
2. (2) $C_C > C_B > C_A$
3. (3) $C_C > C_A > C_B$
4. (4) $C_A > C_C > C_B$
We corrected a printing error in the original paper
Source printed “filled with two dielectric”.

PhysicsJEE Main 28 Jan 2026, Shift 2·Q10·MCQ·Easy–moderate

Identify the correct statements:

A.	Effective capacitance of a series combination of capacitors is always smaller than the smallest capacitance of the capacitor in the combination.
B.	When a dielectric medium is placed between the charged plates of a capacitor, displacement of charges cannot occur due to insulation property of dielectric.
C.	Increasing of area of capacitor plate or decreasing of thickness of dielectric is an alternate method to increase the capacitance.
D.	For a point charge, concentric spherical shells centered at the location of the charge are equipotential surfaces.

Choose the correct answer from the options given below.

(1)A, B and C only
(2)C and D only
(3)A, C and D only
(4)B and D only

PhysicsJEE Main 2 Apr 2026, Shift 1·Q7·MCQ·Easy–moderate
Open
A parallel plate air capacitor has a capacitance $C$ . When it is half filled as shown in figure with a dielectric constant $K = 5$ , the percentage increase in the capacitance is .
1. (1)33.34
2. (2)66.67
3. (3)200
4. (4)400
We corrected a printing error in the original paper
Source printed “half filled as show in figure”.
PhysicsJEE Main 4 Apr 2026, Shift 1·Q15·MCQ·Moderate
Open
A parallel plate air capacitor is connected to a battery. The plates are pulled apart at uniform speed $v$ . If $x$ is the separation between the plates at any instant, then the time rate of change of electrostatic energy of the capacitor is proportional to $x^{\alpha}$ , where $\alpha$ is .
1. (1) $-2$
2. (2)1
3. (3) $-1$
4. (4)2
PhysicsJEE Main 4 Apr 2026, Shift 2·Q12·MCQ·Moderate
Open
From the circuit given below, the capacitance between terminals A and B shown in the circuit is $\mu$ F. (take $C_1 = C_2 = C_3 = 1\ \mu$ F and $C_4 = 2\ \mu$ F.)
1. (1)2
2. (2)7/2
3. (3)7/3
4. (4)5/2
We corrected a printing error in the original paper
Answer corrected; the source key is (2) — the top wire joins A to the $C_2$ / $C_3$ junction, so $C_1 \parallel C_2 = 2\ \mu$ F in series with $C_4 = 2\ \mu$ F gives $1\ \mu$ F, plus $C_3 = 1\ \mu$ F across A–B: $C_{AB} = 2\ \mu$ F (the source's own solution also ends at $2\ \mu$ F).
PhysicsJEE Main 6 Apr 2026, Shift 2·Q15·MCQ·Easy–moderate
Open
A sphere of capacitance 100 pF is charged to a potential of 100 V. Another identical uncharged metal sphere is brought in contact with the charged sphere, then the change in the total energy stored on these spheres, when they touch is $\alpha\times10^{-7}$ J. The value of $\alpha$ is . (combined capacitance of spheres is 200 pF).
1. (1)5
2. (2) $\dfrac52$
3. (3) $\dfrac72$
4. (4) $\dfrac92$
We corrected a printing error in the original paper
Source printed “Another identical undercharged metal sphere”.
PhysicsJEE Main 8 Apr 2026, Shift 2·Q21·Numerical·Easy–moderate
Open
A parallel plate capacitor is having separation between plates 0.885 mm. It has a capacitance of $1\ \mu$ F when the space between the plates is filled with an insulating material of resistivity $1\times10^{13}\ \Omega$ m and resistance $17.7\times10^{14}\ \Omega$ . Relative permittivity of the insulating material is $\alpha\times10^{7}$ . The value of $\alpha$ is .
(Take permittivity of free space $= 8.85\times10^{-12}$ F/m)

Potential

PhysicsJEE Main 22 Jan 2026, Shift 1·Q17·MCQ·Easy–moderate
Open
Electric field in a region is given by $\vec E = Ax\hat i + By\hat j$ , where $A = 10\ \mathrm{V/m^2}$ and $B = 5\ \mathrm{V/m^2}$ . If the electric potential at a point (10, 20) is 500 V, then the electric potential at origin is V.
1. (1)1000
2. (2)500
3. (3)2000
4. (4)0
PhysicsJEE Main 22 Jan 2026, Shift 2·Q5·MCQ·Easy–moderate
Open
Three small identical bubbles of water having same charge on each coalesce to form a bigger bubble. Then the ratio of the potentials on one initial bubble and that on the resultant bigger bubble is :
1. (1) $1 : 3^{1/3}$
2. (2) $1 : 2^{2/3}$
3. (3) $3^{2/3} : 1$
4. (4) $1 : 3^{2/3}$
PhysicsJEE Main 22 Jan 2026, Shift 2·Q17·MCQ·Easy–moderate
Open
Five positive charges each having charge $q$ are placed at the vertices of a pentagon as shown in the figure. The electric potential ( $V$ ) and the electric field ( $\vec E$ ) at the center O of the pentagon due to these five positive charges are :
1. (1) $V = \dfrac{5q}{4\pi\varepsilon_0 r}$ and $\vec E = 0$
2. (2) $V = \dfrac{5q}{4\pi\varepsilon_0 r}$ and $\vec E = \dfrac{5\sqrt3\,q}{8\pi\varepsilon_0 r^2}\hat r$
3. (3) $V = \dfrac{5q}{4\pi\varepsilon_0 r}$ and $\vec E = \dfrac{5q}{4\pi\varepsilon_0 r^2}\hat r$
4. (4) $V = 0$ and $\vec E = 0$
PhysicsJEE Main 24 Jan 2026, Shift 1·Q15·MCQ·Moderate
Open
The electrostatic potential in a charged spherical region of radius $r$ varies as $V = ar^{3} + b$ , where $a$ and $b$ are constants. The total charge in the sphere of unit radius is $\alpha\times\pi a\epsilon_0$ . The value of $\alpha$ is .
(permittivity of vacuum is $\epsilon_0$ )
1. (1) $-12$
2. (2) $-6$
3. (3) $-9$
4. (4) $-8$
PhysicsJEE Main 24 Jan 2026, Shift 1·Q19·MCQ·Easy–moderate
Open
There are three concentric conducting spherical shells A, B and C of radii $a$ , $b$ and $c$ carrying charges $q_1$ , $q_2$ and $q_3$ respectively. The potential of the spheres A, B and C respectively, are :
1. (1) $\dfrac{1}{4\pi\epsilon_0}\left(\dfrac{q_1+q_2+q_3}{a}\right),\ \dfrac{1}{4\pi\epsilon_0}\left(\dfrac{q_1+q_2+q_3}{b}\right),\ \dfrac{1}{4\pi\epsilon_0}\left(\dfrac{q_1+q_2+q_3}{c}\right)$
2. (2) $\dfrac{1}{4\pi\epsilon_0}\left(\dfrac{q_1+q_2+q_3}{a}\right),\ \dfrac{1}{4\pi\epsilon_0}\left(\dfrac{q_1+q_2}{b}+\dfrac{q_3}{c}\right),\ \dfrac{1}{4\pi\epsilon_0}\left(\dfrac{q_1}{a}+\dfrac{q_2}{b}+\dfrac{q_3}{c}\right)$
3. (3) $\dfrac{1}{4\pi\epsilon_0}\left(\dfrac{q_1}{a}+\dfrac{q_2}{b}+\dfrac{q_3}{c}\right),\ \dfrac{1}{4\pi\epsilon_0}\left(\dfrac{q_1+q_2}{b}+\dfrac{q_3}{c}\right),\ \dfrac{1}{4\pi\epsilon_0}\left(\dfrac{q_1+q_2+q_3}{c}\right)$
4. (4) $\dfrac{1}{4\pi\epsilon_0}\left(\dfrac{q_1}{a}+\dfrac{q_2}{b}+\dfrac{q_3}{c}\right),\ \dfrac{1}{4\pi\epsilon_0}\left(\dfrac{q_1+q_2+q_3}{b}\right),\ \dfrac{1}{4\pi\epsilon_0}\left(\dfrac{q_1+q_2+q_3}{c}\right)$
We corrected a printing error in the original paper
Source printed “three co-centric conducting spherical shells A, B and C of radii $a$ , $b$ and $c$ respectively” (the charges used in the options are never stated); corrected to the intended “three concentric conducting spherical shells A, B and C of radii $a$ , $b$ and $c$ carrying charges $q_1$ , $q_2$ and $q_3$ respectively”.
PhysicsJEE Main 28 Jan 2026, Shift 2·Q13·MCQ·Easy
Open
Which one of the following is not a measurable quantity?
1. (1)Voltage difference
2. (2)Resistance
3. (3)Voltage
4. (4)Displacement current
PhysicsJEE Main 2 Apr 2026, Shift 1·Q9·MCQ·Easy–moderate
Open
Two charged conducting spheres $S_1$ and $S_2$ of radii 8 cm and 18 cm are connected to each other by a wire. After equilibrium is established, the electric fields on $S_1$ and $S_2$ spheres are $E_{S1}$ and $E_{S2}$ respectively. The value of $\dfrac{E_{S1}}{E_{S2}}$ is .
1. (1) $\dfrac32$
2. (2) $\dfrac23$
3. (3) $\dfrac49$
4. (4) $\dfrac94$
We corrected a printing error in the original paper
Source printed “the ratio of electric fields on $S_1$ and $S_2$ spheres are $E_{S1}$ and $E_{S2}$ ” (extra words “ratio of”).
PhysicsJEE Main 6 Apr 2026, Shift 1·Q24·Numerical·Easy–moderate
Open
A three coulomb charge moves from the point $(0, -2, -5)$ to the point $(5, 1, 2)$ in an electric field expressed as $\vec E = 2x\hat i + 3y^2\hat j + 4\hat k$ N/C. The work done in moving the charge is J.
PhysicsJEE Main 6 Apr 2026, Shift 2·Q12·MCQ·Easy–moderate
Open
The electric potential as a function of $x$ , $y$ is given by $V = 5(x^2 - y^2)$ V. The electric field at a point (2, 3) m is V/m.
1. (1) $(-20\hat i + 30\hat j)$
2. (2) $(20\hat i - 30\hat j)$
3. (3) $(20\hat i + 45\hat j)$
4. (4) $(-4\hat i + 6\hat j)$

Potential energy

PhysicsJEE Main 21 Jan 2026, Shift 1·Q20·MCQ·Easy–moderate
Open
A point charge of $10^{-8}$ C is placed at origin. The work done in moving a point charge $2\ \mu$ C from point A(4, 4, 2) m to B(2, 2, 1) m is J. ( $\dfrac{1}{4\pi\epsilon_0} = 9\times10^{9}$ in SI units)
1. (1) $45\times10^{-6}$
2. (2)0
3. (3) $30\times10^{-6}$
4. (4) $15\times10^{-6}$
PhysicsJEE Main 21 Jan 2026, Shift 2·Q1·MCQ·Moderate
Open
Consider two identical metallic spheres of radius $R$ each having charge $Q$ and mass $m$ . Their centers have an initial separation of $4R$ . Both the spheres are given an initial speed of $u$ towards each other. The minimum value of u, so that they can just touch each other is : (Take $k = \dfrac{1}{4\pi\epsilon_0}$ and assume $kQ^2 > Gm^2$ where G is the Gravitational constant)
1. (1) $\sqrt{\dfrac{kQ^2}{4mR}\left(1 - \dfrac{Gm^2}{kQ^2}\right)}$
2. (2) $\sqrt{\dfrac{kQ^2}{4mR}\left(1 + \dfrac{Gm^2}{kQ^2}\right)}$
3. (3) $\sqrt{\dfrac{kQ^2}{2mR}\left(1 - \dfrac{Gm^2}{kQ^2}\right)}$
4. (4) $\sqrt{\dfrac{kQ^2}{2mR}\left(1 - \dfrac{Gm^2}{2kQ^2}\right)}$
PhysicsJEE Main 23 Jan 2026, Shift 2·Q7·MCQ·Moderate
Open
Two charges $7\ \mu$ C and $-2\ \mu$ C are placed at $(-9, 0, 0)$ cm and $(9, 0, 0)$ cm respectively in an external field $E = \dfrac{A}{r^2}\,\hat r$ , where $A = 9\times10^{5}\ \mathrm{N\,m^2/C}$ .
Considering the potential at infinity is 0, the electrostatic energy of the configuration is J.
1. (1)1.4
2. (2) $-90.7$
3. (3)49.3
4. (4)24.3
We corrected a printing error in the original paper
Source printed the unit of $A$ as “ $\mathrm{N/C.m^2}$ ” ( $E = A/r^2$ needs $\mathrm{N\,m^2/C}$ ).
PhysicsJEE Main 28 Jan 2026, Shift 1·Q19·MCQ·Easy–moderate
Open
Two point charges of 1 nC and 2 nC are placed at the two corners of equilateral triangle of side 3 cm. The work done in bringing a charge of 3 nC from infinity to the third corner of the triangle is $\mu$ J. $\frac{1}{4\pi\epsilon_0} = 9\times10^{9}\ \mathrm{N.m^2/C^2}$
1. (1)2.7
2. (2)5.4
3. (3)3.3
4. (4)27

Conductors and dielectrics

PhysicsJEE Main 4 Apr 2026, Shift 2·Q13·MCQ·Easy–moderate
Open
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A: In electrostatics, a conductor does not store any net charge inside.
Reason R: Inside the capacitor (with no dielectric medium), the free charge carriers, if placed between the plates of capacitor, experience force and drift.
Choose the correct answer from the options given below.
1. (1)Both A and R are true and R is the correct explanation of A.
2. (2)Both A and R are true but R is NOT the correct explanation of A.
3. (3)A is true but R is false
4. (4)A is false but R is true