Electrostatics & Capacitors · JEE Main previous year questions

2023 63 questions

1. 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

2. 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

3. 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

4. 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

5. Q372023 · 25 Jan 2023 · Shift 2

   Match List I with List II $$\begin{array}{llll}& \text{List I}& & \text{List II}\\ \text{A.}& \text{Gauss’s Law in Electrostatics}& \text{I.}& \oint \vec{E}\cdot \overrightarrow{dl}=-\frac{d{\varphi }_B}{dt}\\ \text{B.}& \text{Faraday’s Law}& \text{II.}& \oint \vec{B}\cdot \overrightarrow{dA}=0\\ \text{C.}& \text{Gauss’s Law in Magnetism}& \text{III.}& \oint \vec{B}\cdot \overrightarrow{dl}={\mu }_0{i}_c+{\mu }_0{ϵ}_0\frac{d{\varphi }_E}{dt}\\ \text{D.}& \text{Ampere-Maxwell Law}& \text{IV.}& \oint \vec{E}\cdot \overrightarrow{ds}=\frac{q}{{ϵ}_0}\end{array}$$ Choose the correct answer from the options given below :

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

6. Q412023 · 25 Jan 2023 · Shift 2

   A point charge of $10\mu \mathrm{C}$ is placed at the origin. At what location on the X-axis should a point charge of $40\mu \mathrm{C}$ be placed so that the net electric field is zero at $x=2$cm on the X-axis?

   1. A.$x=6$ cm
   2. B.$x=8$ cm
   3. C.$x=4$ cm
   4. D.$x=-4$ cm
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   Answer: A

7. Q522023 · 25 Jan 2023 · Shift 2· Numerical answer

   A capacitor has capacitance $5\mu \mathrm{F}$ when its parallel plates are separated by air medium of thickness d. A slab of material of dielectric constant 1.5 having area equal to that of plates but thickness $\frac{d}{2}$ is inserted between the plates. Capacitance of the capacitor in the presence of slab will be ____ $\mu \mathrm{F}$.

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   Answer: 6

8. Q392023 · 24 Jan 2023 · Shift 1

   If two charges ${\mathrm{q}}_1$ and ${\mathrm{q}}_2$ are separated with distance 'd' and placed in a medium of dielectric constant K. What will be the equivalent distance between charges in air for the same electrostatic force?

   1. A.$d\sqrt{k}$
   2. B.$1.5d\sqrt{k}$
   3. C.$k\sqrt{d}$
   4. D.$2d\sqrt{k}$
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   Answer: A

9. Q482023 · 24 Jan 2023 · Shift 1

   If $\vec{E}$ and $\vec{K}$ represent electric field and propagation vectors of the EM waves in vacuum, then magnetic field vector is given by : ($\omega$ - angular frequency) :

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

10. Q572023 · 24 Jan 2023 · Shift 1· Numerical answer

    A stream of positively charged particles having $\frac{q}{m}=2\times 10^{11}\frac{\mathrm{C}}{\mathrm{kg}}$ and velocity ${\vec{v}}_0=3\times 10^7\hat{i}m/s$ is deflected by an electric field $1.8\hat{j}kV/m$. The electric field exists in a region of $10\mathrm{cm}$ along $x$ direction. Due to the electric field, the deflection of the charged particles in the $y$ direction is ____ $\mathrm{mm}$.

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    Answer: 2

11. Q402023 · 24 Jan 2023 · Shift 2

    The electric field and magnetic field components of an electromagnetic wave going through vacuum is described by ${\mathrm{E}}_x={\mathrm{E}}_o\sin (kz-\omega t)$ ${\mathrm{B}}_y={\mathrm{B}}_o\sin (kz-\omega t)$ Then the correct relation between ${\mathrm{E}}_0$ and ${\mathrm{B}}_0$ is given by

    1. A.${\mathrm{E}}_o{\mathrm{B}}_o=\omega k$
    2. B.${\mathrm{E}}_0=k{\mathrm{B}}_0$
    3. C.$k{\mathrm{E}}_0=\omega {\mathrm{B}}_0$
    4. D.$\omega {\mathrm{E}}_0=k{\mathrm{B}}_0$
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    Answer: C

12. Q442023 · 24 Jan 2023 · Shift 2
    
    1. A.$\frac{\lambda }{2{ϵ}_0}$
    2. B.$\frac{\lambda }{{ϵ}_0}$
    3. C.$\frac{2\lambda }{{ϵ}_0}$
    4. D.$\frac{\lambda }{4{ϵ}_0}$
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    Answer: A

13. Q562023 · 24 Jan 2023 · Shift 2· Numerical answer

    A parallel plate capacitor with air between the plates has a capacitance of 15pF. The separation between the plates becomes twice and the space between them is filled with a medium of dielectric constant 3.5. Then the capacitance becomes $\frac{x}{4}\mathrm{pF}$. The value of $x$ is ___________.

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    Answer: 105