Electrostatics & Capacitors · JEE Main previous year questions

2023 63 questions

1. Q342023 · 6 Apr 2023 · Shift 2

   The energy density associated with electric field $\vec{E}$ and magnetic field $\vec{B}$ of an electromagnetic wave in free space is given by (${ϵ}_0-$ permittivity of free space, ${\mu }_0-$ permeability of free space)

   1. A.$U_E=\frac{{ϵ}_0{E}^2}{2},U_B=\frac{B^2}{2{\mu }_0}$
   2. B.$U_E=\frac{E^2}{2{ϵ}_0},U_B=\frac{{\mu }_0{B}^2}{2}$
   3. C.$U_E=\frac{{ϵ}_0{E}^2}{2},U_B=\frac{{\mu }_0{B}^2}{2}$
   4. D.$U_E=\frac{E^2}{2{ϵ}_0},U_B=\frac{B^2}{2{\mu }_0}$
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   Answer: A

2. Q382023 · 6 Apr 2023 · Shift 2

   A capacitor of capacitance $150.0\mu \mathrm{F}$ is connected to an alternating source of emf given by $\mathrm{E}=36\sin (120\pi t)\mathrm{V}$. The maximum value of current in the circuit is approximately equal to :

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

3. Q422023 · 6 Apr 2023 · Shift 2

   A dipole comprises of two charged particles of identical magnitude $q$ and opposite in nature. The mass 'm' of the positive charged particle is half of the mass of the negative charged particle. The two charges are separated by a distance '$l$'. If the dipole is placed in a uniform electric field '$\vec{E}$'; in such a way that dipole axis makes a very small angle with the electric field, '$\vec{E}$'. The angular frequency of the oscillations of the dipole when released is given by:

   1. A.$\sqrt{\frac{3qE}{2ml}}$
   2. B.$\sqrt{\frac{4qE}{ml}}$
   3. C.$\sqrt{\frac{8qE}{3ml}}$
   4. D.$\sqrt{\frac{8qE}{ml}}$
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   Answer: A

4. Q512023 · 6 Apr 2023 · Shift 2· Numerical answer

   Experimentally it is found that $12.8\text{ eV}$ energy is required to separate a hydrogen atom into a proton and an electron. So the orbital radius of the electron in a hydrogen atom is $\frac{9}{x}\times 10^{-10}\text{ m}$. The value of the $x$ is ___________. $\left(1\text{eV}=1.6\times 10^{-19}\text{ J},\frac{1}{4\pi {\epsilon }_0}=9\times 10^9{\text{Nm}}^2/{\text{C}}^2\text{ and electronic charge}=1.6\times 10^{-19}\text{C}\right)$

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   Answer: 16

5. Q532023 · 6 Apr 2023 · Shift 2· Numerical answer
   
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   Answer: 5

6. Q312023 · 1 Feb 2023 · Shift 1
   
   1. A.${\vec{E}}_I=0,{\vec{E}}_{II}=\frac{\sigma }{{ϵ}_0}\hat{n},E_{III}=0$
   2. B.${\vec{E}}_I=\frac{\sigma }{2{ϵ}_0}\hat{n},{\vec{E}}_{II}=0,{\vec{E}}_{III}=\frac{\sigma }{2{ϵ}_0}\hat{n}$
   3. C.${\vec{E}}_I=-\frac{\sigma }{{ϵ}_0}\hat{n},{\vec{E}}_{II}=0,{\vec{E}}_{III}=\frac{\sigma }{{ϵ}_0}\hat{n}$
   4. D.${\vec{E}}_I=\frac{2\sigma }{{ϵ}_0}\hat{n},{\vec{E}}_{II}=0,{\vec{E}}_{III}=\frac{2\sigma }{{ϵ}_0}\hat{n}$
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   Answer: C

7. Q512023 · 1 Feb 2023 · Shift 1· Numerical answer

   Two equal positive point charges are separated by a distance $2a$. The distance of a point from the centre of the line joining two charges on the equatorial line (perpendicular bisector) at which force experienced by a test charge $q_0$ becomes maximum is $\frac{a}{\sqrt{x}}$. The value of $x$ is ________.

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   Answer: 2

8. Q352023 · 31 Jan 2023 · Shift 1
   
   1. A.
   2. B.
   3. C.
   4. D.
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   Answer: D

9. Q562023 · 31 Jan 2023 · Shift 1· Numerical answer
   
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   Answer: 640

10. Q582023 · 31 Jan 2023 · Shift 1· Numerical answer

    In a medium the speed of light wave decreases to 0.2 times to its speed in free space. The ratio of relative permittivity to the refractive index of the medium is $x:1$. The value of $x$ is ___________. $\left(\text{Given speed of light in free space }=3\times 10^8{\text{ m s}}^{-1}\text{ and for the given medium }{\mu }_{\mathrm{r}}=1\right)$

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    Answer: 5

11. Q602023 · 31 Jan 2023 · Shift 2· Numerical answer

    Two parallel plate capacitors $C_1$ and $C_2$ each having capacitance of $10\mu \mathrm{F}$ are individually charged by a $100\text{ V}$ D.C. source. Capacitor $C_1$ is kept connected to the source and then a dielectric slab is inserted between its plates. Capacitor $C_2$ is disconnected from the source and then a dielectric slab is inserted in it. Afterwards the capacitor $C_1$ is also disconnected from the source and the two capacitors are finally connected in parallel combination. The common potential of the combination will be ___________ V. (Assuming Dielectric constant $=10$ )

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    Answer: 55

12. Q382023 · 30 Jan 2023 · Shift 1

    The charge flowing in a conductor changes with time as $Q(t)=\alpha t-\beta t^2+\gamma t^3$. Where $\alpha ,\beta$ and $\gamma$ are constants. Minimum value of current is :

    1. A.$\beta -\frac{{\alpha }^2}{3\gamma }$
    2. B.$\alpha -\frac{3{\beta }^2}{\gamma }$
    3. C.$\alpha -\frac{{\beta }^2}{3\gamma }$
    4. D.$\alpha -\frac{{\gamma }^2}{3\beta }$
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    Answer: C

13. Q402023 · 30 Jan 2023 · Shift 1

    Electric field in a certain region is given by $\vec{\mathrm{E}}=\left(\frac{\mathrm{A}}{x^2}\hat{i}+\frac{\mathrm{B}}{y^3}\hat{j}\right)$. The SI unit of A and B are :

    1. A.$\mathrm{N}{\mathrm{m}}^2\mathrm{C};\mathrm{N}{\mathrm{m}}^3\mathrm{C}$
    2. B.$\mathrm{N}{\mathrm{m}}^3{\mathrm{C}}^{-1};\mathrm{N}{\mathrm{m}}^2{\mathrm{C}}^{-1}$
    3. C.$\mathrm{N}{\mathrm{m}}^3\mathrm{C};\mathrm{N}{\mathrm{m}}^2\mathrm{C}$
    4. D.$\mathrm{N}{\mathrm{m}}^2{\mathrm{C}}^{-1};\mathrm{N}{\mathrm{m}}^3{\mathrm{C}}^{-1}$
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    Answer: D

14. Q412023 · 30 Jan 2023 · Shift 1

    Two isolated metallic solid spheres of radii R and 2R are charged such that both have same charge density $\sigma$. The spheres are then connected by a thin conducting wire. If the new charge density of the bigger sphere is ${\sigma }^{\prime }$. The ratio $\frac{{\sigma }^{\prime }}{\sigma }$ is :

    1. A.$\frac{5}{3}$
    2. B.$\frac{5}{6}$
    3. C.$\frac{9}{4}$
    4. D.$\frac{4}{3}$
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    Answer: B

15. Q492023 · 30 Jan 2023 · Shift 1

    In a series LR circuit with ${\mathrm{X}}_{\mathrm{L}}=\mathrm{R}$, power factor ${\mathrm{P}}_1$. If a capacitor of capacitance C with ${\mathrm{X}}_{\mathrm{C}}={\mathrm{X}}_{\mathrm{L}}$ is added to the circuit the power factor becomes ${\mathrm{P}}_2$. The ratio of ${\mathrm{P}}_1$ to ${\mathrm{P}}_2$ will be :

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

16. Q602023 · 30 Jan 2023 · Shift 1· Numerical answer

    A capacitor of capacitance $900\mu \text{F}$ is charged by a $100\text{ V}$ battery. The capacitor is disconnected from the battery and connected to another uncharged identical capacitor such that one plate of uncharged capacitor connected to positive plate and another plate of uncharged capacitor connected to negative plate of the charged capacitor. The loss of energy in this process is measured as $x\times 10^{-2}\text{ J}$. The value of $x$ is ___________.

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    Answer: 225

17. Q542023 · 29 Jan 2023 · Shift 1· Numerical answer

    A point charge $q_1=4q_0$ is placed at origin. Another point charge $q_2=-q_0$ is placed at $x=12$ cm. Charge of proton is $q_0$. The proton is placed on $x$ axis so that the electrostatic force on the proton is zero. In this situation, the position of the proton from the origin is ____ cm.

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    Answer: 24

18. Q382023 · 29 Jan 2023 · Shift 2

    Given below are two statements : Statement I : Electromagnetic waves are not deflected by electric and magnetic field. Statement II : The amplitude of electric field and the magnetic field in electromagnetic waves are related to each other as $E_0=\sqrt{\frac{{\mu }_0}{{\epsilon }_0}}{B}_0$. In the light of the above statements, choose the correct answer from the options given below :

    1. A.Both Statement I and Statement II are true
    2. B.Statement I is true and Statement II is false
    3. C.Both Statement I and Statement II are false
    4. D.Statement I is false but Statement II is true
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    Answer: B

19. Q472023 · 29 Jan 2023 · Shift 2

    A point charge $2\times 10^{-2}\mathrm{C}$ is moved from P to S in a uniform electric field of $30\mathrm{N}{\mathrm{C}}^{-1}$ directed along positive x-axis. If coordinates of P and S are (1, 2, 0) m and (0, 0, 0) m respectively, the work done by electric field will be

    1. A.600 mJ
    2. B.$-1200$ mJ
    3. C.1200 mJ
    4. D.$-600$ mJ
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    Answer: D

20. Q532023 · 29 Jan 2023 · Shift 2· Numerical answer

    An inductor of inductance $2\mu \mathrm{H}$ is connected in series with a resistance, a variable capacitor and an AC source of frequency 7 kHz. The value of capacitance for which maximum current is drawn into the circuit $\frac{1}{x}\mathrm{F}$, where the value of $x$ is ____. (Take $\pi =\frac{22}{7}$)

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    Answer: 3872

21. Q582023 · 29 Jan 2023 · Shift 2· Numerical answer

    For a charged spherical ball, electrostatic potential inside the ball varies with $r$ as $V=2a{r}^2+b$. Here, $a$ and $b$ are constant and r is the distance from the center. The volume charge density inside the ball is $-\lambda a\epsilon$. The value of $\lambda$ is __________. $\epsilon =\text{permittivity of the medium}$

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    Answer: 12

22. Q312023 · 25 Jan 2023 · Shift 1

    A parallel plate capacitor has plate area $40\mathrm{c}{\mathrm{m}}^2$ and plates separation $2\mathrm{mm}$. The space between the plates is filled with a dielectric medium of a thickness $1\mathrm{mm}$ and dielectric constant 5. The capacitance of the system is :

    1. A.$10{\epsilon }_0\mathrm{F}$
    2. B.$24{\epsilon }_0\mathrm{F}$
    3. C.$\frac{3}{10}{\epsilon }_0\mathrm{F}$
    4. D.$\frac{10}{3}{\epsilon }_0\mathrm{F}$
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    Answer: D

23. Q432023 · 25 Jan 2023 · Shift 1

    An electromagnetic wave is transporting energy in the negative $z$ direction. At a certain point and certain time the direction of electric field of the wave is along positive $y$ direction. What will be the direction of the magnetic field of the wave at that point and instant?

    1. A.Negative direction of $y$
    2. B.Positive direction of $z$
    3. C.Positive direction of $x$
    4. D.Negative direction $x$
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    Answer: C

24. Q452023 · 25 Jan 2023 · Shift 1

    In an LC oscillator, if values of inductance and capacitance become twice and eight times, respectively, then the resonant frequency of oscillator becomes $x$ times its initial resonant frequency ${\omega }_0$. The value of $x$ is :

    1. A.1/4
    2. B.1/16
    3. C.4
    4. D.16
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    Answer: A

25. Q602023 · 25 Jan 2023 · Shift 1· Numerical answer

    A uniform electric field of 10 N/C is created between two parallel charged plates (as shown in figure). An electron enters the field symmetrically between the plates with a kinetic energy 0.5 eV. The length of each plate is 10 cm. The angle $(\theta )$ of deviation of the path of electron as it comes out of the field is ____ (in degree).

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    Answer: 45