Electrostatics & Capacitors · JEE Main previous year questions

2024 51 questions

1. Q472024 · 1 Feb 2024 · Shift 1

   In series LCR circuit, the capacitance is changed from $C$ to $4C$. To keep the resonance frequency unchanged, the new inductance should be:

   1. A.increased by $2\mathrm{L}$
   2. B.reduced by $\frac{1}{4}\mathrm{L}$
   3. C.reduced by $\frac{3}{4}\mathrm{L}$
   4. D.increased to $4\mathrm{L}$
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   Answer: C

2. Q532024 · 1 Feb 2024 · Shift 1· Numerical answer

   Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle $\theta$ with each other. When suspended in water the angle remains the same. If density of the material of the sphere is $1.5g/cc$, the dielectric constant of water will be ____. (Take density of water $=1g/cc$ )

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   Answer: 3

3. Q602024 · 1 Feb 2024 · Shift 1· Numerical answer

   The current in a conductor is expressed as $I=3t^2+4t^3$, where $I$ is in Ampere and $t$ is in second. The amount of electric charge that flows through a section of the conductor during $t=1\mathrm{s}$ to $t=2\mathrm{s}$ is ____ C.

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   Answer: 22

4. Q342024 · 1 Feb 2024 · Shift 2
   
   1. A.$3:2$
   2. B.$5:2$
   3. C.$2:5$
   4. D.$2:3$
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   Answer: C

5. Q522024 · 1 Feb 2024 · Shift 2· Numerical answer
   
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   Answer: 60

6. Q542024 · 1 Feb 2024 · Shift 2· Numerical answer

   Suppose a uniformly charged wall provides a uniform electric field of $2\times 10^4\text{ N/C}$ normally. A charged particle of mass $2\text{ g}$ being suspended through a silk thread of length $20\text{ cm}$ and remain stayed at a distance of $10\text{ cm}$ from the wall. Then the charge on the particle will be $\frac{1}{\sqrt{x}}\mu \text{C}$ where $x=$ ________ . $[\text{use }g=10{\text{ m/s}}^2]$

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   Answer: 3

7. Q322024 · 31 Jan 2024 · Shift 1

   Two charges $q$ and $3q$ are separated by a distance '$r$' in air. At a distance $x$ from charge $q$, the resultant electric field is zero. The value of $x$ is :

   1. A.$\frac{r}{3(1+\sqrt{3})}$
   2. B.$\frac{(1+\sqrt{3})}{r}$
   3. C.$\frac{r}{(1+\sqrt{3})}$
   4. D.$r(1+\sqrt{3})$
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   Answer: C

8. Q492024 · 31 Jan 2024 · Shift 1

   In a plane EM wave, the electric field oscillates sinusoidally at a frequency of $5\times 10^{10}\mathrm{Hz}$ and an amplitude of $50\mathrm{V}{\mathrm{m}}^{-1}$. The total average energy density of the electromagnetic field of the wave is : [Use ${\epsilon }_0=8.85\times 10^{-12}{\mathrm{C}}^2/N{\mathrm{m}}^2$ ]

   1. A.$4.425\times 10^{-8}\mathrm{J}{\mathrm{m}}^{-3}$
   2. B.$2.212\times 10^{-10}\mathrm{J}{\mathrm{m}}^{-3}$
   3. C.$2.212\times 10^{-8}\mathrm{J}{\mathrm{m}}^{-3}$
   4. D.$1.106\times 10^{-8}\mathrm{J}{\mathrm{m}}^{-3}$
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   Answer: D

9. Q532024 · 31 Jan 2024 · Shift 1· Numerical answer

   A parallel plate capacitor with plate separation $5\mathrm{mm}$ is charged up by a battery. It is found that on introducing a dielectric sheet of thickness $2\mathrm{mm}$, while keeping the battery connections intact, the capacitor draws $25\%$ more charge from the battery than before. The dielectric constant of the sheet is ____.

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   Answer: 2

10. Q462024 · 31 Jan 2024 · Shift 2

    Force between two point charges $q_1$ and $q_2$ placed in vacuum at '$r$' cm apart is $F$. Force between them when placed in a medium having dielectric constant $K=5$ at '$r/5$' cm apart will be:

    1. A.$5F$
    2. B.$25F$
    3. C.$F/5$
    4. D.$F/25$
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    Answer: A

11. Q582024 · 31 Jan 2024 · Shift 2· Numerical answer
    
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    Answer: 27

12. Q372024 · 30 Jan 2024 · Shift 1

    The electrostatic potential due to an electric dipole at a distance '$r$' varies as :

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

13. Q402024 · 30 Jan 2024 · Shift 1

    The electric field of an electromagnetic wave in free space is represented as $\vec{E}=E_0\cos (\omega t-kz)\hat{i}$. The corresponding magnetic induction vector will be :

    1. A.$\vec{B}=E_{0}C\cos (\omega t+kz)\hat{j}$
    2. B.$\vec{B}=\frac{E_0}{C}\cos (\omega t-kz)\hat{j}$
    3. C.$\vec{B}=E_{0}C\cos (\omega t-kz)\hat{j}$
    4. D.$\vec{B}=\frac{E_0}{C}\cos (\omega t+kz)\hat{j}$
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    Answer: B

14. Q542024 · 30 Jan 2024 · Shift 1· Numerical answer

    A capacitor of capacitance $C$ and potential $\mathrm{V}$ has energy $\mathrm{E}$. It is connected to another capacitor of capacitance $2C$ and potential $2\text{ V}$. Then the loss of energy is $\frac{x}{3}\mathrm{E}$, where $x$ is _________.

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    Answer: 2

15. Q352024 · 29 Jan 2024 · Shift 1

    A capacitor of capacitance $100\mu \text{F}$ is charged to a potential of $12\text{ V}$ and connected to a $6.4\text{ mH}$ inductor to produce oscillations. The maximum current in the circuit would be :

    1. A.$2.0\text{ A}$
    2. B.$3.2\text{ A}$
    3. C.$1.5\text{ A}$
    4. D.$1.2\text{ A}$
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    Answer: C

16. Q392024 · 29 Jan 2024 · Shift 1

    Two charges of $5Q$ and $-2Q$ are situated at the points $(3a,0)$ and $(-5a,0)$ respectively. The electric flux through a sphere of radius '$4a$' having center at origin is :

    1. A.$\frac{2Q}{{\epsilon }_0}$
    2. B.$\frac{7Q}{{\epsilon }_0}$
    3. C.$\frac{3Q}{{\epsilon }_0}$
    4. D.$\frac{5Q}{{\epsilon }_0}$
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    Answer: D

17. Q442024 · 29 Jan 2024 · Shift 1

    Match List I with List II | | List - I | | List - II | | :--- | :--- | :--- | :--- | | (A) | $\oint \vec{B}\cdot \overrightarrow{dl}={\mu }_o{i}_c+{\mu }_o{\epsilon }_o\frac{d{\varphi }_E}{dt}$ | (I) | Gauss' law for electricity | | (B) | $\oint \vec{E}\cdot \overrightarrow{dl}=\frac{d{\varphi }_B}{dt}$ | (II) | Gauss' law for magnetism | | (C) | $\oint \vec{E}\cdot \overrightarrow{dA}=\frac{Q}{{\epsilon }_o}$ | (III) | Faraday law | | (D) | $\oint \vec{B}\cdot \overrightarrow{dA}=0$ | (IV) | Ampere - Maxwell law | Choose the correct answer from the options given below:

    1. A.A-IV, B-III, C-I, D-II
    2. B.A-I, B-II, C-III, D-IV
    3. C.A-IV, B-I, C-III, D-II
    4. D.A-II, B-III, C-I, D-IV
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    Answer: A

18. Q482024 · 29 Jan 2024 · Shift 1

    The electric current through a wire varies with time as $I=I_0+\beta t$, where $I_0=20\text{ A}$ and $\beta =3\text{ A/s}$. The amount of electric charge crossed through a section of the wire in $20\text{ s}$ is :

    1. A.$80\text{ C}$
    2. B.$800\text{ C}$
    3. C.$1000\text{ C}$
    4. D.$1600\text{ C}$
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    Answer: C

19. Q532024 · 29 Jan 2024 · Shift 1· Numerical answer

    An electron is moving under the influence of the electric field of a uniformly charged infinite plane sheet S having surface charge density $+\sigma$. The electron at $t=0$ is at a distance of $1\text{ m}$ from $S$ and has a speed of $1\text{ m/s}$. The maximum value of $\sigma$ if the electron strikes $S$ at $t=1\text{ s}$ is $\alpha \left[\frac{m{\epsilon }_0}{e}\right]\frac{\text{C}}{{\text{m}}^2}$, the value of $\alpha$ is _______.

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    Answer: 8

20. Q372024 · 29 Jan 2024 · Shift 2

    An electric field is given by $(6\hat{i}+5\hat{j}+3\hat{k})\text{N/C}$. The electric flux through a surface area $30\hat{i}{\text{ m}}^2$ lying in YZ-plane (in SI unit) is :

    1. A.60
    2. B.90
    3. C.180
    4. D.150
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    Answer: C

21. Q522024 · 29 Jan 2024 · Shift 2· Numerical answer
    
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    Answer: 36

22. Q432024 · 27 Jan 2024 · Shift 1

    An electric charge $10^{-6}\mu \text{C}$ is placed at origin $(0,0)\text{ m}$ of $X-Y$ co-ordinate system. Two points P and Q are situated at $(\sqrt{3},\sqrt{3})\text{m}$ and $(\sqrt{6},0)\text{m}$ respectively. The potential difference between the points P and Q will be :

    1. A.$\sqrt{3}\text{ V}$
    2. B.$\sqrt{6}\text{ V}$
    3. C.$0\text{ V}$
    4. D.$3\text{ V}$
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    Answer: C

23. Q522024 · 27 Jan 2024 · Shift 1· Numerical answer

    A thin metallic wire having cross sectional area of $10^{-4}{\text{ m}}^2$ is used to make a ring of radius $30\text{ cm}$. A positive charge of $2\pi \text{ C}$ is uniformly distributed over the ring, while another positive charge of $30\text{ pC}$ is kept at the centre of the ring. The tension in the ring is _____ $\text{N}$; provided that the ring does not get deformed (neglect the influence of gravity). (given, $\frac{1}{4\pi {ϵ}_0}=9\times 10^9\text{ SI units}$)

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    Answer: 3

24. Q592024 · 27 Jan 2024 · Shift 1· Numerical answer
    
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    Answer: 400

25. Q442024 · 27 Jan 2024 · Shift 2

    Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : Work done by electric field on moving a positive charge on an equipotential surface is always zero. Reason (R) : Electric lines of forces are always perpendicular to equipotential surfaces. 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.(A) is correct but (R) is not correct
    3. C.Both (A) and (R) are correct but (R) is not the correct explanation of (A)
    4. D.(A) is not correct but (R) is correct
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    Answer: A