Electrostatics & Capacitors · JEE Main previous year questions

2024 51 questions

1. Q312024 · 9 Apr 2024 · Shift 1

   A plane EM wave is propagating along $x$ direction. It has a wavelength of $4\text{ mm}$. If electric field is in $y$ direction with the maximum magnitude of $60{\text{ Vm}}^{-1}$, the equation for magnetic field is :

   1. A.${\mathrm{B}}_z=2\times 10^{-7}\sin \left[\frac{\pi }{2}(x-3\times 10^8\mathrm{t})\right]\hat{\mathrm{k}}\mathrm{T}$
   2. B.${\mathrm{B}}_z=2\times 10^{-7}\sin \left[\frac{\pi }{2}\times 10^3(x-3\times 10^8\mathrm{t})\right]\hat{\mathrm{k}}\mathrm{T}$
   3. C.${\mathrm{B}}_z=60\sin \left[\frac{\pi }{2}(x-3\times 10^8\mathrm{t})\right]\hat{\mathrm{k}}\mathrm{T}$
   4. D.${\mathrm{B}}_x=60\sin \left[\frac{\pi }{2}(x-3\times 10^8\mathrm{t})\right]\hat{\mathrm{i}}\mathrm{T}$
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   Answer: B

2. Q422024 · 9 Apr 2024 · Shift 1
   
   1. A.$\frac{11{ϵ}_o\mathrm{A}}{20\mathrm{d}}$
   2. B.$\frac{13{ϵ}_o\mathrm{A}}{17\mathrm{d}}$
   3. C.$\frac{18{ϵ}_o\mathrm{A}}{11\mathrm{d}}$
   4. D.$\frac{11{ϵ}_o\mathrm{A}}{18\mathrm{d}}$
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   Answer: D

3. Q492024 · 9 Apr 2024 · Shift 1

   A bulb and a capacitor are connected in series across an ac supply. A dielectric is then placed between the plates of the capacitor. The glow of the bulb :

   1. A.becomes zero
   2. B.remains same
   3. C.increases
   4. D.decreases
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   Answer: C

4. Q522024 · 9 Apr 2024 · Shift 1· Numerical answer

   At the centre of a half ring of radius $\mathrm{R}=10\text{ cm}$ and linear charge density $4{\text{ nC m}}^{-1}$, the potential is $x\pi \text{V}$. The value of $x$ is ______.

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   Answer: 36

5. Q362024 · 9 Apr 2024 · Shift 2

   The magnetic field in a plane electromagnetic wave is $B_y=(3.5\times 10^{-7})\sin (1.5\times 10^{3}x+0.5\times 10^{11}t)\mathrm{T}$. The corresponding electric field will be :

   1. A.$E_z=105\sin (1.5\times 10^{3}x+0.5\times 10^{11}t)\mathrm{V}{\mathrm{m}}^{-1}$
   2. B.$E_y=10.5\sin (1.5\times 10^{3}x+0.5\times 10^{11}t)\mathrm{V}{\mathrm{m}}^{-1}$
   3. C.$E_y=1.17\sin (1.5\times 10^{3}x+0.5\times 10^{11}t)\mathrm{V}{\mathrm{m}}^{-1}$
   4. D.$E_z=1.17\sin (1.5\times 10^{3}x+0.5\times 10^{11}t)\mathrm{V}{\mathrm{m}}^{-1}$
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   Answer: A

6. Q382024 · 9 Apr 2024 · Shift 2
   
   1. A.$\frac{q}{{ϵ}_0}$
   2. B.$\frac{3q}{{ϵ}_0}$
   3. C.$\frac{5q}{{ϵ}_0}$
   4. D.$\frac{4q}{{ϵ}_0}$
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   Answer: D

7. Q522024 · 9 Apr 2024 · Shift 2· Numerical answer
   
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   Answer: 16

8. Q322024 · 8 Apr 2024 · Shift 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:

   1. A.$ab$
   2. B.$\frac{b}{a}$
   3. C.$\frac{a}{b}$
   4. D.$\sqrt{ab}$
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   Answer: C

9. Q522024 · 8 Apr 2024 · Shift 1· Numerical answer

   An electric field, $\vec{E}=\frac{2\hat{i}+6\hat{j}+8\hat{k}}{\sqrt{6}}$ passes through the surface of $4{\text{ m}}^2$ area having unit vector $\hat{n}=\left(\frac{2\hat{i}+\hat{j}+\hat{k}}{\sqrt{6}}\right)$. The electric flux for that surface is ________ $\text{Vm}$.

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   Answer: 12

10. Q592024 · 8 Apr 2024 · Shift 1· Numerical answer

    An electron with kinetic energy $5\text{ eV}$ enters a region of uniform magnetic field of $3\mu \text{T}$ perpendicular to its direction. An electric field E is applied perpendicular to the direction of velocity and magnetic field. The value of E, so that electron moves along the same path, is ________ ${\text{NC}}^{-1}$. (Given, mass of electron $=9\times 10^{-31}\text{ kg}$, electric charge $=1.6\times 10^{-19}\text{ C}$)

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    Answer: 4

11. Q342024 · 8 Apr 2024 · Shift 2

    If ${ϵ}_{\mathrm{o}}$ is the permittivity of free space and $\mathrm{E}$ is the electric field, then ${ϵ}_{\mathrm{o}}{\mathrm{E}}^2$ has the dimensions :

    1. A.$[{\mathrm{ML}}^{-1}{\mathrm{T}}^{-2}]$
    2. B.$[{\mathrm{ML}}^2{\mathrm{T}}^{-2}]$
    3. C.$[{\mathrm{M}}^0{\mathrm{L}}^{-2}\mathrm{TA}]$
    4. D.$[{\mathrm{M}}^{-1}{\mathrm{L}}^{-3}{\mathrm{T}}^4{\mathrm{A}}^2]$
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    Answer: A

12. Q412024 · 8 Apr 2024 · Shift 2

    A capacitor has air as dielectric medium and two conducting plates of area $12\mathrm{c}{\mathrm{m}}^2$ and they are $0.6\mathrm{cm}$ apart. When a slab of dielectric having area $12\mathrm{c}{\mathrm{m}}^2$ and $0.6\mathrm{cm}$ thickness is inserted between the plates, one of the conducting plates has to be moved by $0.2\mathrm{cm}$ to keep the capacitance same as in previous case. The dielectric constant of the slab is : (Given ${ϵ}_0=8.834\times 10^{-12}F/m$)

    1. A.$1.50$
    2. B.$0.66$
    3. C.$1.33$
    4. D.$1$
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    Answer: A

13. Q512024 · 8 Apr 2024 · Shift 2· Numerical answer

    An alternating emf $\mathrm{E}=110\sqrt{2}\sin 100t\mathrm{volt}$ is applied to a capacitor of $2\mu \mathrm{F}$, the rms value of current in the circuit is ____ $\mathrm{mA}$.

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    Answer: 22

14. Q522024 · 8 Apr 2024 · Shift 2· Numerical answer
    
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    Answer: 5

15. Q432024 · 6 Apr 2024 · Shift 2

    Two identical conducting spheres P and S with charge Q on each, repel each other with a force $16\mathrm{N}$. A third identical uncharged conducting sphere R is successively brought in contact with the two spheres. The new force of repulsion between P and S is :

    1. A.$1\mathrm{N}$
    2. B.$6\mathrm{N}$
    3. C.$12\mathrm{N}$
    4. D.$4\mathrm{N}$
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    Answer: B

16. Q552024 · 6 Apr 2024 · Shift 2· Numerical answer
    
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    Answer: 80

17. Q492024 · 5 Apr 2024 · Shift 2

    The electrostatic force $\left({\vec{F}}_1\right)$ and magnetic force $\left({\vec{F}}_2\right)$ acting on a charge $q$ moving with velocity $v$ can be written :

    1. A.${\vec{F}}_1=q\vec{B}$, ${\vec{F}}_2=q(\vec{B}\times \vec{v})$
    2. B.${\vec{F}}_1=q\vec{V}\cdot \vec{E}$, ${\vec{F}}_2=q(\vec{B}\cdot \vec{V})$
    3. C.${\vec{F}}_1=q\vec{E}$, ${\vec{F}}_2=q(\vec{V}\times \vec{B})$
    4. D.${\vec{F}}_1=q\vec{E}$, ${\vec{F}}_2=q(\vec{B}\times \vec{V})$
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    Answer: C

18. Q512024 · 5 Apr 2024 · Shift 2· Numerical answer
    
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    Answer: 16

19. Q372024 · 4 Apr 2024 · Shift 1

    In an ac circuit, the instantaneous current is zero, when the instantaneous voltage is maximum. In this case, the source may be connected to : A. pure inductor. B. pure capacitor. C. pure resistor. D. combination of an inductor and capacitor. Choose the correct answer from the options given below :

    1. A.A, B and C only
    2. B.A and B only
    3. C.A, B and D only
    4. D.B, C and D only
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    Answer: C

20. Q452024 · 4 Apr 2024 · Shift 1

    The electric field in an electromagnetic wave is given by $\vec{\mathrm{E}}=\hat{i}40\cos \omega (t-z/c){\mathrm{NC}}^{-1}$. The magnetic field induction of this wave is (in SI unit) :

    1. A.$\vec{\mathrm{B}}=\hat{j}\frac{40}{c}\cos \omega (t-z/c)$
    2. B.$\vec{\mathrm{B}}=\hat{i}\frac{40}{c}\cos \omega (t-z/c)$
    3. C.$\vec{B}=\hat{j}40\cos \omega (t-z/c)$
    4. D.$\vec{\mathrm{B}}=\hat{k}\frac{40}{c}\cos \omega (t-z/c)$
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    Answer: A

21. Q522024 · 4 Apr 2024 · Shift 1· Numerical answer

    An infinite plane sheet of charge having uniform surface charge density $+{\sigma }_{s}C/{\mathrm{m}}^2$ is placed on $x$-$y$ plane. Another infinitely long line charge having uniform linear charge density $+{\lambda }_{e}C/m$ is placed at $z=4\mathrm{m}$ plane and parallel to $y$-axis. If the magnitude values $|{\sigma }_s|=2|{\lambda }_e|$ then at point $(0,0,2)$, the ratio of magnitudes of electric field values due to sheet charge to that of line charge is $\pi \sqrt{n}:1$. The value of $n$ is ____.

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    Answer: 16

22. Q452024 · 4 Apr 2024 · Shift 2

    A charge $q$ is placed at the center of one of the surfaces of a cube. The flux linked with the cube is:

    1. A.$\frac{q}{2{ϵ}_0}$
    2. B.$\text{Zero}$
    3. C.$\frac{q}{4{ϵ}_0}$
    4. D.$\frac{q}{8{ϵ}_0}$
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    Answer: A

23. Q602024 · 4 Apr 2024 · Shift 2· Numerical answer

    A parallel plate capacitor of capacitance $12.5\text{ pF}$ is charged by a battery connected between its plates to potential difference of $12.0\text{ V}$. The battery is now disconnected and a dielectric slab $({ϵ}_r=6)$ is inserted between the plates. The change in its potential energy after inserting the dielectric slab is ________ $\times 10^{-12}\text{ J}$.

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    Answer: 750

24. Q412024 · 1 Feb 2024 · Shift 1

    A parallel plate capacitor has a capacitance $\mathrm{C}=200\mathrm{pF}$. It is connected to $230\mathrm{V}$ ac supply with an angular frequency $300rad/s$. The rms value of conduction current in the circuit and displacement current in the capacitor respectively are :

    1. A.$14.3\mu \mathrm{A}$ and $143\mu \mathrm{A}$
    2. B.$13.8\mu \mathrm{A}$ and $13.8\mu \mathrm{A}$
    3. C.$13.8\mu \mathrm{A}$ and $138\mu \mathrm{A}$
    4. D.$1.38\mu \mathrm{A}$ and $1.38\mu \mathrm{A}$
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    Answer: B

25. Q442024 · 1 Feb 2024 · Shift 1

    Two identical capacitors have same capacitance $C$. One of them is charged to the potential $V$ and other to the potential $2\mathrm{V}$. The negative ends of both are connected together. When the positive ends are also joined together, the decrease in energy of the combined system is :

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