Electrostatics & Capacitors · JEE Main previous year questions

2025 43 questions

1. Q382025 · 8 Apr 2025 · Shift 2

   Two metal spheres of radius $\mathbf{R}$ and $3\mathbf{R}$ have same surface charge density $\mathbf{\sigma }$. If they are brought in contact and then separated, the surface charge density on smaller and bigger sphere becomes ${\mathbf{\sigma }}_1$ and ${\mathbf{\sigma }}_2$, respectively. The ratio $\frac{{\sigma }_1}{{\sigma }_2}$ is

   1. A.$\frac{1}{3}$
   2. B.$\frac{1}{9}$
   3. C.$9$
   4. D.$3$
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   Answer: D

2. Q402025 · 8 Apr 2025 · Shift 2

   Given below are two statements: one is labelled as Assertion $\mathbf{A}$ and the other is labelled as Reason $\mathbf{R}$ Assertion A : Work done in moving a test charge between two points inside a uniformly charged spherical shell is zero, no matter which path is chosen. Reason R : Electrostatic potential inside a uniformly charged spherical shell is constant and is same as that on the surface of the shell. 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.Both A and R are true but R is NOT the correct explanation of A
   4. D.A is false but R is true
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   Answer: B

3. Q412025 · 8 Apr 2025 · Shift 2
   
   1. A.B and C Only
   2. B.A and C Only
   3. C.D and E Only
   4. D.A, B and C Only
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   Answer: D

4. Q422025 · 8 Apr 2025 · Shift 2

   An infinitely long wire has uniform linear charge density $\lambda =2nC/m$. The net flux through a Gaussian cube of side length $\sqrt{3}\mathrm{cm}$, if the wire passes through any two corners of the cube, that are maximally displaced from each other, would be $x{\mathrm{Nm}}^2{\mathrm{C}}^{-1}$, where $x$ is: [Neglect any edge effects and use $\frac{1}{4\pi {\epsilon }_0}=9\times 10^9\mathrm{SI}\mathrm{units}$]

   1. A.$6.48\pi$
   2. B.$0.72\pi$
   3. C.$1.44\pi$
   4. D.$2.16\pi$
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   Answer: D

5. Q482025 · 8 Apr 2025 · Shift 2· Numerical answer
   
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   Answer: 15

6. Q302025 · 4 Apr 2025 · Shift 1

   Current passing through a wire as function of time is given as $I(t)=0.02t+0.01\mathrm{A}$. The charge that will flow through the wire from $t=1\mathrm{s}$ to $t=2\mathrm{s}$ is

   1. A.$0.02\mathrm{C}$
   2. B.$0.07\mathrm{C}$
   3. C.$0.06\mathrm{C}$
   4. D.$0.04\mathrm{C}$
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   Answer: D

7. Q342025 · 4 Apr 2025 · Shift 1
   
   1. A.$|{\vec{E}}_A|=|{\vec{E}}_B|;{\vec{E}}_C>{\vec{E}}_D$
   2. B.${\vec{E}}_A={\vec{E}}_B;{\vec{E}}_C={\vec{E}}_D$
   3. C.${\vec{E}}_C\ne {\vec{E}}_D;{\vec{E}}_A>{\vec{E}}_B$
   4. D.${\vec{E}}_A>{\vec{E}}_B;{\vec{E}}_C={\vec{E}}_D$
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   Answer: C

8. Q452025 · 4 Apr 2025 · Shift 1

   Two small spherical balls of mass 10 g each with charges $-2\mu \mathrm{C}$ and $2\mu \mathrm{C}$, are attached to two ends of very light rigid rod of length 20 cm . The arrangement is now placed near an infinite nonconducting charge sheet with uniform charge density of $100\mu C/{\mathrm{m}}^2$ such that length of rod makes an angle of $30^{\circ }$ with electric field generated by charge sheet. Net torque acting on the rod is: (Take ${\epsilon }_0:8.85\times 10^{-12}{\mathrm{C}}^2/N{\mathrm{m}}^2$ )

   1. A.$1.12\mathrm{Nm}$
   2. B.$2.24\mathrm{Nm}$
   3. C.$11.2\mathrm{Nm}$
   4. D.$112\mathrm{Nm}$
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   Answer: A

9. Q502025 · 4 Apr 2025 · Shift 1· Numerical answer
   
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   Answer: 64

10. Q292025 · 4 Apr 2025 · Shift 2
    
    1. A.$2\mathrm{E}$
    2. B.Zero
    3. C.$\mathrm{E}/2$
    4. D.$\sqrt{2}\mathrm{E}$
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    Answer: D

11. Q372025 · 4 Apr 2025 · Shift 2
    
    1. A.$9\mu \mathrm{F}$
    2. B.$30\mu \mathrm{F}$
    3. C.$7.5\mu \mathrm{F}$
    4. D.$22.5\mu \mathrm{F}$
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    Answer: A

12. Q482025 · 4 Apr 2025 · Shift 2· Numerical answer

    If an optical medium possesses a relative permeability of $\frac{10}{\pi }$ and relative permittivity of $\frac{1}{0.0885}$, then the velocity of light is greater in vacuum than that in this medium by ____ times. $({\mu }_0=4\pi \times 10^{-7}H/m,{ϵ}_0=8.85\times 10^{-12}F/m,c=3\times 10^{8}m/s)$

    Show answer

    Answer: 6

13. Q342025 · 3 Apr 2025 · Shift 1
    
    1. A.$\frac{{\epsilon }_0({\epsilon }_1+{\epsilon }_2)}{2}$
    2. B.$\frac{{\epsilon }_1{\epsilon }_2^2}{({\epsilon }_1+{\epsilon }_2{)}^2}$
    3. C.$\frac{4{\epsilon }_1{\epsilon }_2}{({\epsilon }_1+{\epsilon }_2{)}^2}$
    4. D.$\frac{{\epsilon }_1{\epsilon }_2}{{\epsilon }_1+{\epsilon }_2}$
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    Answer: C

14. Q432025 · 3 Apr 2025 · Shift 1

    The electrostatic potential on the surface of uniformly charged spherical shell of radius $\mathrm{R}=10\mathrm{cm}$ is $120\mathrm{V}$ . The potential at the centre of shell, at a distance $\mathrm{r}=5\mathrm{cm}$ from centre, and at a distance $\mathrm{r}=15\mathrm{cm}$ from the centre of the shell respectively, are:

    1. A.$0\mathrm{V},120\mathrm{V},40\mathrm{V}$
    2. B.$120\mathrm{V},120\mathrm{V},80\mathrm{V}$
    3. C.$40\mathrm{V},40\mathrm{V},80\mathrm{V}$
    4. D.$0\mathrm{V},0\mathrm{V},80\mathrm{V}$
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    Answer: B

15. Q332025 · 3 Apr 2025 · Shift 2

    Using a battery, a 100 pF capacitor is charged to 60 V and then the battery is removed. After that, a second uncharged capacitor is connected to the first capacitor in parallel. If the final voltage across the second capacitor is 20 V , its capacitance is: (in pF )

    1. A.600
    2. B.100
    3. C.400
    4. D.200
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    Answer: D

16. Q262025 · 2 Apr 2025 · Shift 1
    
    1. A.$\frac{3\sigma q}{4{ϵ}_0}$
    2. B.$\frac{3\sigma q}{2{ϵ}_0}$
    3. C.$\frac{\sigma q}{4{ϵ}_0}$
    4. D.$\frac{\sigma q}{2{ϵ}_0}$
    Show answer

    Answer: B

17. Q362025 · 2 Apr 2025 · Shift 1

    A point charge $+q$ is placed at the origin. A second point charge $+9q$ is placed at $(\mathrm{d},0,0)$ in Cartesian coordinate system. The point in between them where the electric field vanishes is:

    1. A.(3d/4, 0, 0)
    2. B.(d/4, 0, 0)
    3. C.(4d/3, 0, 0)
    4. D.(d/3, 0, 0)
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    Answer: B

18. Q282025 · 2 Apr 2025 · Shift 2

    Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : Net dipole moment of a polar linear isotropic dielectric substance is not zero even in the absence of an external electric field. Reason (R) : In absence of an external electric field, the different permanent dipoles of a polar dielectric substance are oriented in random directions. In the light of the above statements, choose the most appropriate answer from the options given below :

    1. A.Both (A) and (R) are correct and (R) is the correct explanation of (A)
    2. B.Both (A) and (R) are correct but (R) is not the correct explanation of (A)
    3. C.(A) is not correct but (R) is correct
    4. D.(A) is correct but (R) is not correct
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    Answer: C

19. Q412025 · 2 Apr 2025 · Shift 2

    Consider a circular loop that is uniformly charged and has a radius $a\sqrt{2}$. Find the position along the positive $z$-axis of the cartesian coordinate system where the electric field is maximum if the ring was assumed to be placed in $xy$ plane at the origin :

    1. A.$\mathrm{a}$
    2. B.$a/2$
    3. C.0
    4. D.$a/\sqrt{2}$
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    Answer: A

20. Q322025 · 29 Jan 2025 · Shift 2

    A plane electromagnetic wave propagates along the $+x$ direction in free space. The components of the electric field, $\vec{E}$ and magnetic field, $\vec{B}$ vectors associated with the wave in Cartesian frame are

    1. A.$E_x,B_y$
    2. B.$E_y,B_x$
    3. C.$E_y,B_z$
    4. D.$E_z,B_y$
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    Answer: C

21. Q422025 · 29 Jan 2025 · Shift 2

    A point charge causes an electric flux of $-2\times 10^4\mathrm{N}{\mathrm{m}}^2{\mathrm{C}}^{-1}$ to pass through a spherical Gaussian surface of $8.0\mathrm{cm}$ radius, centred on the charge. The value of the point charge is : (Given ${ϵ}_0=8.85\times 10^{-12}{\mathrm{C}}^2{\mathrm{N}}^{-1}{\mathrm{m}}^{-2}$ )

    1. A.$17.7\times 10^{-8}\mathrm{C}$
    2. B.$-17.7\times 10^{-8}\mathrm{C}$
    3. C.$15.7\times 10^{-8}\mathrm{C}$
    4. D.$-15.7\times 10^{-8}\mathrm{C}$
    Show answer

    Answer: B

22. Q432025 · 29 Jan 2025 · Shift 2
    
    1. A.$q_1=10\mu \mathrm{C},q_2=20\mu \mathrm{C}$
    2. B.$q_1=15\mu \mathrm{C},q_2=30\mu \mathrm{C}$
    3. C.$q_1=20\mu \mathrm{C},q_2=10\mu \mathrm{C}$
    4. D.$q_1=30\mu \mathrm{C},q_2=15\mu \mathrm{C}$
    Show answer

    Answer: A

23. Q442025 · 29 Jan 2025 · Shift 2
    
    1. A.Torque on dipole is zero and net force is directed away from the sheet.
    2. B.Potential energy of dipole is minimum and torque is zero.
    3. C.Potential energy and torque both are maximum.
    4. D.Torque on dipole is zero and net force acts towards the sheet.
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    Answer: B

24. Q492025 · 29 Jan 2025 · Shift 2· Numerical answer

    A parallel plate capacitor consisting of two circular plates of radius $10\mathrm{cm}$ is being charged by a constant current of $0.15\mathrm{A}$ . If the rate of change of potential difference between the plates is $7\times 10^{8}V/s$ then the integer value of the distance between the parallel plates is ( Take, ${ϵ}_0=9\times 10^{-12}\frac{\mathrm{F}}{\mathrm{m}},\pi =\frac{22}{7}$ ) ____ $\mu \mathrm{m}$.

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    Answer: 1320

25. Q352025 · 28 Jan 2025 · Shift 1

    Consider a long thin conducting wire carrying a uniform current I. A particle having mass " $m$ " and charge " $q$ " is released at a distance " $a$ " from the wire with a speed $v_0$ along the direction of current in the wire. The particle gets attracted to the wire due to magnetic force. The particle turns round when it is at distance $x$ from the wire. The value of $x$ is [ ${\mu }_0$ is vacuum permeability]

    1. A.$a\left[1-\frac{m{v}_0}{2q{\mu }_0\mathrm{I}}\right]$
    2. B.$a{\mathrm{e}}^{-\frac{4\pi m{v}_0}{q{\mu }_0\mathrm{I}}}$
    3. C.$a\left[1-\frac{mv}{q}{\mu }_0\mathrm{I}\right]$
    4. D.$\frac{a}{2}$
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    Answer: B