Electrostatics & Capacitors · JEE Main previous year questions

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2026 52 questions

Q372026 · 28 Jan 2026 · Shift 1
The electric field of an electromagnetic wave travelling through a medium is given by $E (x, t) = 25 sin (2.0 \times 1 0^{15} t - 1 0^{7} x) \overset{n}{^}$ then the refractive index of the medium is ____ . (All given measurement are in SI units)
1. A.2
2. B.1.2
3. C.1.5
4. D.1.7
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Answer: C
Q412026 · 28 Jan 2026 · Shift 1
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 ____ $μ J$ . $\frac{1}{4 π ϵ _{0}} = 9 \times 1 0^{9} N \cdot m^{2} / C^{2}$
1. A.3.3
2. B.27
3. C.2.7
4. D.5.4
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Answer: C
Q332026 · 28 Jan 2026 · Shift 2
A plane electromagnetic wave is moving in free space with velocity $c = 3 \times 1 0^{8} m/s$ and its electric field is given as $E = 54 sin (k z - ω t) \hat{j} V/m$ , where $\hat{j}$ is the unit vector along y-axis. The magnetic field vector $B$ of the wave is :
1. A. $- 1.8 \times 1 0^{- 7} sin (k z - ω t) \hat{i} T$
2. B. $+ 1.8 \times 1 0^{- 7} sin (k z - ω t) \hat{i} T$
3. C. $1.4 \times 1 0^{- 7} sin (k z - ω t) \hat{k} T$
4. D. $1.4 \times 1 0^{- 7} sin (k z - ω t) \hat{i} T$
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Answer: A
Q352026 · 28 Jan 2026 · Shift 2
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.A, C and D Only
2. B.A, B and C Only
3. C.B and D Only
4. D.C and D Only
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Answer: A
Q362026 · 28 Jan 2026 · Shift 2
Identify the correct statements : A. Electrostatic field lines form closed loops. B. The electric field lines point radially outward when charge is greater than zero. C. The Gauss - Law is valid only for inverse-square force. D. The work done in moving a charged particle in a static electric field around a closed path is zero. E. The motion of a particle under Coulomb's force must take place in a plane. Choose the correct answer from the options given below :
1. A.A, C, E Only
2. B.A, B, D, E Only
3. C.B, C, D, E Only
4. D.A, B, C, D Only
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Answer: C
Q272026 · 24 Jan 2026 · Shift 1
The electrostatic potential in a charged spherical region of radius $r$ varies as $V = a r^{3} + b$ , where $a$ and $b$ are constants. The total charge in the sphere of unit radius is $α \times π a ϵ_{0}$ . The value of $α$ is ____ . (permittivity of vacuum is $ϵ_{0}$ )
1. A.-12
2. B.-8
3. C.-9
4. D.-6
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Answer: A
Q412026 · 24 Jan 2026 · Shift 1
There are three concentric conducting spherical shells $A$ , $B$ and $C$ of radii $a$ , $b$ and $c$ respectively ( $c > b > a$ ) and they are charged with charge $q_{1}$ , $q_{2}$ and $q_{3}$ respectively. The potentials of the spheres $A$ , $B$ and $C$ respectively, are :
1. A. $\frac{1}{4 π ϵ _{o}} (\frac{q _{1}}{a} + \frac{q _{2}}{b} + \frac{q _{3}}{c})$ , $\frac{1}{4 π ϵ _{o}} (\frac{q _{1} + q _{2} + q _{3}}{b})$ , $\frac{1}{4 π ϵ _{o}} (\frac{q _{1} + q _{2} + q _{3}}{c})$
2. B. $\frac{1}{4 π ϵ _{o}} (\frac{q _{1} + q _{2} + q _{3}}{a})$ , $\frac{1}{4 π ϵ _{o}} (\frac{q _{1} + q _{2} + q _{3}}{b})$ , $\frac{1}{4 π ϵ _{o}} (\frac{q _{1} + q _{2} + q _{3}}{c})$
3. C. $\frac{1}{4 π ϵ _{o}} (\frac{q _{1} + q _{2} + q _{3}}{a})$ , $\frac{1}{4 π ϵ _{o}} (\frac{q _{1} + q _{2}}{b} + \frac{q _{3}}{c})$ , $\frac{1}{4 π ϵ _{o}} (\frac{q _{1}}{a} + \frac{q _{2}}{b} + \frac{q _{3}}{c})$
4. D. $\frac{1}{4 π ϵ _{o}} (\frac{q _{1}}{a} + \frac{q _{2}}{b} + \frac{q _{3}}{c})$ , $\frac{1}{4 π ϵ _{o}} (\frac{q _{1} + q _{2}}{b} + \frac{q _{3}}{c})$ , $\frac{1}{4 π ϵ _{o}} (\frac{q _{1} + q _{2} + q _{3}}{c})$
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Answer: D
Q422026 · 24 Jan 2026 · Shift 1
Three charges $+ 2 q$ , $+ 3 q$ and $- 4 q$ are situated at $(0, - 3 a)$ , $(2 a, 0)$ and $(- 2 a, 0)$ respectively in the $x y$ plane. The resultant dipole moment about origin is ____ .
1. A. $2 q a (7 \hat{i} - 3 \hat{j})$
2. B. $2 q a (3 \hat{j} - 7 \hat{i})$
3. C. $2 q a (3 \hat{i} - 7 \hat{j})$
4. D. $2 q a (3 \hat{j} - \hat{i})$
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Answer: A
Q312026 · 23 Jan 2026 · Shift 1
Match List - I with List - II. | List - I (Relation) | List - II (Law) | | :--- | :--- | | A. $\oint E \cdot d l = - \frac{d}{d t} \oint B \cdot d a$ | I. Ampere's circuital law | | B. $\oint B \cdot d l = μ_{0} (I + ϵ_{0} \frac{d ϕ _{E}}{d t})$ | II. Faraday's laws of electromagnetic induction | | C. $\oint E \cdot d a = \frac{1}{ϵ _{0}} \int_{V} ρ d v$ | III. Ampere - Maxwell law | | D. $\oint B \cdot d l = μ_{0} I$ | IV. Gauss's law of electrostatics | Choose the correct answer from the options given below :
1. A.A-I, B-IV, C-III, D-II
2. B.A-II, B-III, C-IV, D-I
3. C.A-IV, B-I, C-II, D-III
4. D.A-II, B-III, C-I, D-IV
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Answer: B
Q362026 · 23 Jan 2026 · Shift 1
1. A. $\frac{3 q}{2 ϵ _{0}}$
2. B. $\frac{3 q}{4 ϵ _{0}}$
3. C. $\frac{q}{ϵ _{0}}$
4. D. $\frac{3 q}{ϵ _{0}}$
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Answer: B
Q382026 · 23 Jan 2026 · Shift 1
Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Consider a ferromagnetic material : Assertion (A) : The individual atoms in a ferromagnetic material possess a magnetic dipole moment and interact with one another in such a way that they spontaneously align themselves forming domains. Reason (R) : At high enough temperature, the domain structure of ferromagnetic material disintegrates. Thus, magnetization will disappear at high enough temperature known as Curie temperature. In the light of the above statements, choose the correct answer from the options given below :
1. A.(A) is true but (R) is false
2. B.Both (A) and (R) are true and (R) is the correct explanation of (A)
3. C.(A) is false but (R) is true
4. D.Both (A) and (R) are true but (R) is not the correct explanation of (A)
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Answer: D
Q472026 · 23 Jan 2026 · Shift 1· Numerical answer
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Answer: 8
Q482026 · 23 Jan 2026 · Shift 1· Numerical answer
The equation of the electric field of an electromagnetic wave propagating through free space is given by : $E = 377 sin (6.27 \times 1 0^{3} t - 2.09 \times 1 0^{- 5} x) N/C$ The average power of the electromagnetic wave is $(\frac{1}{α}) W/m^{2}$ . The value of $α$ is ____ . $(Take \frac{μ _{0}}{ε _{0}} = 377 in SI units)$
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Answer: 2
Q502026 · 23 Jan 2026 · Shift 1· Numerical answer
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Answer: 50
Q292026 · 23 Jan 2026 · Shift 2
1. A. $\frac{9}{16} 2 \times 1 0^{5}$
2. B. $\frac{9}{16} 2 \times 1 0^{4}$
3. C. $92 \times 1 0^{4}$
4. D. $4.5 2 \times 1 0^{4}$
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Answer: B
Q332026 · 23 Jan 2026 · Shift 2
The ratio of speeds of electromagnetic waves in vacuum and a medium, having dielectric constant $k = 3$ and permeability of $μ = 2 μ_{0}$ , is ( $μ_{0} =$ permeability of vacuum)
1. A. $6 : 1$
2. B. $3 : 2$
3. C. $6 : 1$
4. D. $36 : 1$
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Answer: C
Q362026 · 23 Jan 2026 · Shift 2
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. A.1.0
2. B.2.5
3. C.1.5
4. D.2.0
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Answer: D
Q392026 · 23 Jan 2026 · Shift 2
Two charges $7 μ C$ and $- 2 μ C$ are placed at $(- 9, 0, 0) cm$ and $(9, 0, 0) cm$ respectively in an external field $E = \frac{A}{r ^{2}} \overset{r}{^}$ , where $A = 9 \times 1 0^{5} N/C \cdot m^{2}$ . Considering the potential at infinity is 0 , the electrostatic energy of the configuration is _____ J.
1. A.49.3
2. B.1.4
3. C.24.3
4. D.-90.7
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Answer: A
Q292026 · 22 Jan 2026 · Shift 1
Electric field in a region is given by $E = A x \hat{i} + B y \hat{j}$ , where $A = 10 V/ m^{2}$ and $B = 5 V/ m^{2}$ . If the electric potential at a point $(10, 20)$ is 500 V , then the electric potential at origin is ____ V.
1. A.1000
2. B.0
3. C.2000
4. D.500
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Answer: C
Q352026 · 22 Jan 2026 · Shift 1
A simple pendulum has a bob with mass $m$ and charge $q$ . The pendulum string has negligible mass. When a uniform and horizontal electric field $E$ is applied, the tension in the string changes. The final tension in the string, when pendulum attains an equilibrium position is ____.
1. A. $m g - q E$
2. B. $m^{2} g^{2} + q^{2} E^{2}$
3. C. $m g + q E$
4. D. $m^{2} g^{2} - q^{2} E^{2}$
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Answer: B
Q422026 · 22 Jan 2026 · Shift 1
1. A. $- (\frac{5 Q}{8 π ϵ _{0} R ^{2}}) (\hat{i} - 3 \hat{j})$
2. B. $\frac{Q}{4 π ϵ _{o} R ^{2}} (3 \hat{i} - \hat{j})$
3. C. $- \frac{Q}{4 π ϵ _{o} R ^{2}} (3 \hat{i} - \hat{j})$
4. D. $- \frac{5 Q}{8 π ϵ _{o} R ^{2}} (\hat{i} + 3 \hat{j})$
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Answer: C
Q472026 · 22 Jan 2026 · Shift 1· Numerical answer
The electric field of a plane electromagnetic wave, travelling in an unknown nonmagnetic medium is given by, $E_{y} = 20 sin (3 \times 1 0^{6} x - 4.5 \times 1 0^{14} t) V/m$ (where $x, t$ and other values have S.I. units). The dielectric constant of the medium is ____ (speed of light in free space is $3 \times 1 0^{8} m/s$ )
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Answer: 4
Q322026 · 21 Jan 2026 · Shift 1
The electric field in a plane electromagnetic wave is given by : $E_{y} = 69 sin [0.6 \times 1 0^{3} x - 1.8 \times 1 0^{11} t] V/m .$ The expression for magnetic field associated with this electromagnetic wave is ____ T.
1. A. $B_{z} = 2.3 \times 1 0^{- 7} sin [0.6 \times 1 0^{3} x - 1.8 \times 1 0^{11} t]$
2. B. $B_{z} = 2.3 \times 1 0^{- 7} sin [0.6 \times 1 0^{3} x + 1.8 \times 1 0^{11} t]$
3. C. $B_{y} = 2.3 \times 1 0^{- 7} sin [0.6 \times 1 0^{3} x - 1.8 \times 1 0^{11} t]$
4. D. $B_{y} = 69 sin [0.6 \times 1 0^{3} x + 1.8 \times 1 0^{11} t]$
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Answer: A
Q332026 · 21 Jan 2026 · Shift 1
A parallel plate capacitor has capacitance $C$ , when there is vacuum within the parallel plates. A sheet having thickness $(\frac{1}{3})^{rd}$ of the separation between the plates and relative permittivity $K$ is introduced between the plates. The new capacitance of the system is :
1. A. $\frac{3 C K ^{2}}{( 2 K + 1 ) ^{2}}$
2. B. $\frac{4 K C}{3 K - 1}$
3. C. $\frac{C K}{2 + K}$
4. D. $\frac{3 K C}{2 K + 1}$
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Answer: D
Q422026 · 21 Jan 2026 · Shift 2
A capacitor C is first charged fully with potential difference of $V_{0}$ and disconnected from the battery. The charged capacitor is connected across an inductor having inductance L. In $t$ s, 25% of the initial energy in the capacitor is transferred to the inductor. The value of $t$ is ____ s.
1. A. $\frac{π L C}{3}$
2. B. $\frac{π L C}{2}$
3. C. $π \frac{L C}{2}$
4. D. $\frac{π L C}{6}$
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Answer: D