Electrostatics & Capacitors · JEE Main previous year questions

2026 52 questions

1. Q272026 · 8 Apr 2026 · Shift 2

   Consider the equation $H=\frac{x^p{ϵ}^q{E}^r}{t^s}$ Where $H=\text{magnetic field}$; $E=\text{electric field}$, $ϵ=\text{permittivity}$, $x=\text{distance}$, $t=\text{time}$ The values of $p,q,r$ and $s$ respectively are :

   1. A.$1,1,1,1$
   2. B.$-1,1,2,1$
   3. C.$1,-1,-2,1$
   4. D.$-1,-2,-2,1$
   Show answer

   Answer: A

2. Q412026 · 8 Apr 2026 · Shift 2

   Two point charges $q_1=3\mu \mathrm{C}$ and $q_2=-4\mu \mathrm{C}$ are placed at points $\left(2\hat{i}+3\hat{j}+3\hat{k}\right)$ and $\left(\hat{i}+\hat{j}+\hat{k}\right)$ respectively. Force on charge $q_2$ is ____ $\mathrm{N}$. $\left(\text{Take }\frac{1}{4\pi {ϵ}_0}=9\times 10^9\text{SI Units}\right)$

   1. A.$\left(12\hat{i}+24\hat{j}+24\hat{k}\right)\times 10^{-3}$
   2. B.$\left(4\hat{i}+8\hat{j}+8\hat{k}\right)\times 10^{-3}$
   3. C.$\left(3\hat{i}+6\hat{j}+6\hat{k}\right)\times 10^{-3}$
   4. D.$\left(-4\hat{i}-8\hat{j}-8\hat{k}\right)\times 10^{-3}$
   Show answer

   Answer: B

3. Q462026 · 8 Apr 2026 · Shift 2· Numerical answer

   A parallel plate capacitor is having separation between plates $0.885\mathrm{mm}$. It has a capacitance of $1\mu \mathrm{F}$ when the space between the plates is filled with an insulating material of resistivity $1\times 10^{13}\Omega \mathrm{m}$ and resistance $17.7\times 10^{14}\Omega$. Relative permittivity of the insulating material is $\alpha \times 10^7$. The value of $\alpha$ is ____ . (Take permittivity of free space $=8.85\times 10^{-12}F/m$)

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   Answer: 2

4. Q492026 · 8 Apr 2026 · Shift 2· Numerical answer
   
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   Answer: 200

5. Q382026 · 6 Apr 2026 · Shift 1

   A thin half ring of radius $35\mathrm{cm}$ is uniformly charged with a total charge of $Q$ coulomb. If the magnitude of the electric field at centre of the half ring is $100V/m$, then the value of $Q$ is ____ $\mathrm{nC}$. (${\in }_o=8.85\times 10^{-12}{\mathrm{C}}^2/N{\mathrm{m}}^2$ and $\pi =3.14$)

   1. A.2.14
   2. B.2.44
   3. C.3.25
   4. D.0.7
   Show answer

   Answer: A

6. Q492026 · 6 Apr 2026 · Shift 1· Numerical answer

   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 ____ $\mathrm{J}$.

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   Answer: 186

7. Q312026 · 6 Apr 2026 · Shift 2

   For an electromagnetic wave propagating through vacuum, $\vec{k}$, $\vec{E}$ and $\omega$ represent propagation vector, electric field and angular frequency, respectively. The magnetic field associated with this wave is represented by :

   1. A.$\frac{\vec{E}\times \vec{k}}{\omega }$
   2. B.$\frac{\vec{k}\times \vec{E}}{\omega }$
   3. C.$\omega (\vec{E}\times \vec{k})$
   4. D.$\omega (\vec{k}\times \vec{E})$
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   Answer: B

8. Q342026 · 6 Apr 2026 · Shift 2

   A cylindrical vessel of $40\text{ cm}$ radius is completely filled with water and its capacity is $528{\text{ dm}}^3$ ($\text{dm}:\text{decimeter}$) The vessel is placed on a solid block of exactly same height as vessel. If a small hole is made at $70\text{ cm}$ below the top of water level, then horizontal range of water falling on the ground in the beginning is ________ $\text{cm}$.

   1. A.$120\sqrt{2}$
   2. B.$140\sqrt{2}$
   3. C.$140\sqrt{3}$
   4. D.$120\sqrt{3}$
   Show answer

   Answer: B

9. Q372026 · 6 Apr 2026 · Shift 2

   The electric potential as a function of $x$, $y$ is given by $V=5(x^2-y^2)\text{ V}$. The electric field at a point $(2,3)\text{ m}$ is ________ $\text{V/m}$.

   1. A.$(-20\hat{i}+30\hat{j})$
   2. B.$(20\hat{i}-30\hat{j})$
   3. C.$(20\hat{i}+45\hat{j})$
   4. D.$(-4\hat{i}+6\hat{j})$
   Show answer

   Answer: A

10. Q402026 · 6 Apr 2026 · Shift 2

    A sphere of capacitance $100\text{ pF}$ is charged to a potential of $100\text{ V}$. 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 $\alpha \times 10^{-7}\text{ J}$. The value of $\alpha$ is ________. (combined capacitance of spheres is $200\text{ pF}$)

    1. A.$5$
    2. B.$\frac{5}{2}$
    3. C.$\frac{7}{2}$
    4. D.$\frac{9}{2}$
    Show answer

    Answer: B

11. Q352026 · 5 Apr 2026 · Shift 1

    An electron of mass $m$ is moving in an electric field $\vec{E}=-2E_o\hat{i}$ ($E_o=\text{constant}>0$), with an initial velocity $\vec{V}=v_o\hat{i}$ ($v_o=\text{constant}>0$). If ${\lambda }_o=\frac{h}{4m{v}_o}$ , its de Broglie wavelength at time $t$ is ____. ($e=\text{charge of electron}$)

    1. A.$\frac{4{\lambda }_o}{\left[1-\frac{E_{o}et}{2m{v}_o}\right]}$
    2. B.$\frac{4{\lambda }_o}{\left[1+\frac{E_{o}et}{2m{v}_o}\right]}$
    3. C.$\frac{4{\lambda }_o}{\left[1+\frac{2E_{o}et}{m{v}_o}\right]}$
    4. D.$\frac{4{\lambda }_o}{\left[1-\frac{2E_{o}et}{m{v}_o}\right]}$
    Show answer

    Answer: C

12. Q372026 · 5 Apr 2026 · Shift 1

    A displacement current of $4.0\mathrm{A}$ can be set up in the space between two parallel plates of $6\mu \mathrm{F}$ capacitor. The rate of change of potential difference across the plates of the capacitor is nearly $\alpha \times 10^{6}V/s$. The value of $\alpha$ is ____.

    1. A.0.58
    2. B.0.67
    3. C.0.82
    4. D.0.75
    Show answer

    Answer: B

13. Q372026 · 5 Apr 2026 · Shift 2
    
    1. A.0.5
    2. B.1.5
    3. C.0
    4. D.2
    Show answer

    Answer: A

14. Q382026 · 5 Apr 2026 · Shift 2

    A particle of charge $q$ and mass $m$ is projected from origin with an initial velocity $\vec{v}=\left(\frac{v_0}{\sqrt{2}}\hat{x}+\frac{v_0}{\sqrt{2}}\hat{y}\right)$. There exists a uniform magnetic field $\vec{B}=B_0\hat{z}$ and a space varying electric field $\vec{E}=E_0{\mathrm{e}}^{-\lambda x}\hat{x}$ within the region $0⩽x⩽L$. After travelling a distance such that $x$-coordinate has changed from $x=0$ to $x=L$, the change in the kinetic energy is ____.

    1. A.$\frac{q{E}_0}{\lambda }\left[1-{\mathrm{e}}^{-\lambda L}\right]$
    2. B.$\left(\frac{v_{0}q{B}_0}{2\lambda }\right)\left[2-{\mathrm{e}}^{-2\lambda L}\right]$
    3. C.$\frac{q{E}_0}{\lambda }\left[1+{\mathrm{e}}^{-\lambda L}\right]$
    4. D.$q\left(\frac{E_0+v_0{B}_0}{\lambda }\right)\left[1-{\mathrm{e}}^{-\lambda L/2}\right]$
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    Answer: A

15. Q402026 · 4 Apr 2026 · Shift 1

    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. A.$-2$
    2. B.1
    3. C.$-1$
    4. D.2
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    Answer: A

16. Q502026 · 4 Apr 2026 · Shift 1· Numerical answer

    An inductor of $10\text{ mH}$, capacitor of $0.1\mu \text{F}$ and a resistor of $100\Omega$ are connected in series across an $a.c$ power supply $220\text{ V}$, $70\text{ Hz}$. The power factor of the given circuit is $0.5$. The difference in the inductive reactance and capacitance reactance is $\sqrt{3}\alpha \Omega$. The value of $\alpha$ is ________.

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    Answer: 100

17. Q372026 · 4 Apr 2026 · Shift 2
    
    1. A.2
    2. B.7/2
    3. C.7/3
    4. D.5/2
    Show answer

    Answer: A

18. Q382026 · 4 Apr 2026 · Shift 2

    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. A.Both A and R are true and R is the correct explanation of A
    2. B.Both A and R are true but R is NOT the correct explanation of A
    3. C.A is true but R is false
    4. D.A is false but R is true
    Show answer

    Answer: B

19. Q402026 · 4 Apr 2026 · Shift 2

    A magnetic field vector in an electromagnetic wave is represented by $\vec{B}=B_0\sin \left(2\pi \nu t-\frac{2\pi x}{\lambda }\right)\hat{j}$. Its associated electric field vector is ____.

    1. A.$\vec{E}=-\nu \lambda B_0\sin \left(2\pi \nu t-\frac{2\pi x}{\lambda }\right)\hat{k}$
    2. B.$\vec{E}=-\nu \lambda B_0\sin \left(2\pi \nu t-\frac{2\pi x}{\lambda }\right)\hat{i}$
    3. C.$\vec{E}=\nu \lambda B_0\sin \left(2\pi \nu t-\frac{2\pi x}{\lambda }\right)\hat{k}$
    4. D.$\vec{E}=\nu \lambda B_0\sin \left(2\pi \nu t-\frac{2\pi x}{\lambda }\right)\hat{i}$
    Show answer

    Answer: A

20. Q322026 · 2 Apr 2026 · Shift 1
    
    1. A.33.34
    2. B.66.67
    3. C.200
    4. D.400
    Show answer

    Answer: B

21. Q342026 · 2 Apr 2026 · Shift 1

    Two charged conducting spheres ${\mathrm{S}}_1$ and ${\mathrm{S}}_2$ of radii $8\mathrm{cm}$ and $18\mathrm{cm}$ are connected to each other by a wire. After equilibrium is established, the ratio of electric fields on ${\mathrm{S}}_1$ and ${\mathrm{S}}_2$ spheres are ${\mathrm{E}}_{S1}$ and ${\mathrm{E}}_{S2}$ respectively. The value of $\frac{{\mathrm{E}}_{S1}}{{\mathrm{E}}_{S2}}$ is ____.

    1. A.$\frac{3}{2}$
    2. B.$\frac{2}{3}$
    3. C.$\frac{4}{9}$
    4. D.$\frac{9}{4}$
    Show answer

    Answer: D

22. Q362026 · 2 Apr 2026 · Shift 1
    
    1. A.
    2. B.
    3. C.
    4. D.
    Show answer

    Answer: B

23. Q292026 · 2 Apr 2026 · Shift 2

    A particle having charge $10^{-9}\mathrm{C}$ moving in $x$-$y$ plane in fields of $0.4\hat{j}N/C$ and $4\times 10^{-3}\hat{k}\mathrm{T}$ experiences a force of $(4\hat{i}+2\hat{j})\times 10^{-10}\mathrm{N}$. The velocity of the particle at that instant is ____ $m/s$.

    1. A.$50\hat{i}+100\hat{j}$
    2. B.$100\hat{i}+50\hat{j}$
    3. C.$-50\hat{i}+100\hat{j}$
    4. D.$50\hat{i}-100\hat{j}$
    Show answer

    Answer: A

24. Q372026 · 2 Apr 2026 · Shift 2

    An electromagnetic wave travels in free space along the $x$-direction. At a particular point in space and time, $\vec{B}=2\times 10^{-7}\hat{j}\mathrm{T}$ is associated with this wave. The value of corresponding electric field $\vec{E}$ at this point is ____ $V/m$.

    1. A.$60\hat{k}$
    2. B.$-60\hat{k}$
    3. C.$30\hat{k}$
    4. D.$-600\hat{k}$
    Show answer

    Answer: B

25. Q402026 · 2 Apr 2026 · Shift 2

    Two point charges $8\mu \mathrm{C}$ and $-2\mu \mathrm{C}$ are located at $x=2\mathrm{cm}$ and $x=4\mathrm{cm}$, respectively on the $x$-axis. The ratio of electric flux due to these charges through two spheres of radii $3\mathrm{cm}$ and $5\mathrm{cm}$ with their centers at the origin is ____.

    1. A.$4:1$
    2. B.$3:4$
    3. C.$4:3$
    4. D.$4:5$
    Show answer

    Answer: C