Electrostatics & Capacitors · JEE Main previous year questions

2020 47 questions

1. Q292020 · 6 Sept 2020 · Shift 1
   
   1. A.
   2. B.
   3. C.
   4. D.
   Show answer

   Answer: B

2. Q362020 · 6 Sept 2020 · Shift 1

   An electron is moving along +x direction with a velocity of $6\times 10^6\mathrm{m}{\mathrm{s}}^{-1}$. It enters a region of uniform electric field of $300V/cm$ pointing along +y direction. The magnitude and direction of the magnetic field set up in this region such that the electron keeps moving along the x direction will be :

   1. A.$3\times 10^{-4}\mathrm{T}$, along $-z$ direction
   2. B.$5\times 10^{-3}\mathrm{T}$, along $-z$ direction
   3. C.$5\times 10^{-3}\mathrm{T}$, along $+z$ direction
   4. D.$3\times 10^{-4}\mathrm{T}$, along $+z$ direction
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   Answer: C

3. Q422020 · 6 Sept 2020 · Shift 1
   
   1. A.$\frac{x_1^3}{x_2^3}$
   2. B.$\frac{x_2^2}{x_1^2}$
   3. C.$\frac{x_1}{x_2}$
   4. D.$\frac{x_2}{x_1}$
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   Answer: C

4. Q472020 · 6 Sept 2020 · Shift 1· Numerical answer

   Suppose that intensity of a laser is $\frac{315}{\pi }W/{\mathrm{m}}^2$. The rms electric field, in units of V/m associated with this source is close to the nearest integer is ______ . $$({ϵ}_0=8.86\times 10^{-12}{\mathrm{C}}^2\mathrm{N}{\mathrm{m}}^{-2};c=3\times 10^8\mathrm{m}{\mathrm{s}}^{-1})$$

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   Answer: 194

5. Q262020 · 6 Sept 2020 · Shift 2

   For a plane electromagnetic wave, the magnetic field at a point x and time t is $$\vec{B}(x,t)=\left[1.2\times 10^{-7}\sin \left(0.5\times 10^{3}x+1.5\times 10^{11}t\right)\hat{k}\right]\mathrm{T}$$ The instantaneous electric field $\vec{E}$ corresponding to $\vec{B}$ is : (speed of light $c=3\times 10^8\mathrm{m}{\mathrm{s}}^{-1}$)

   1. A.$\vec{E}(x,t)=\left[36\sin \left(1\times 10^{3}x+1.5\times 10^{11}t\right)\hat{i}\right]\frac{\mathrm{V}}{\mathrm{m}}$
   2. B.$\vec{E}(x,t)=\left[36\sin \left(0.5\times 10^{3}x+1.5\times 10^{11}t\right)\hat{k}\right]\frac{\mathrm{V}}{\mathrm{m}}$
   3. C.$\vec{E}(x,t)=\left[36\sin \left(1\times 10^{3}x+0.5\times 10^{11}t\right)\hat{j}\right]\frac{\mathrm{V}}{\mathrm{m}}$
   4. D.$\vec{E}(x,t)=\left[-36\sin \left(0.5\times 10^{3}x+1.5\times 10^{11}t\right)\hat{j}\right]\frac{\mathrm{V}}{\mathrm{m}}$
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   Answer: D

6. Q392020 · 6 Sept 2020 · Shift 2

   Consider the force F on a charge 'q' due to a uniformly charged spherical shell of radius R carrying charge Q distributed uniformly over it. Which one of the following statements is true for F, if 'q' is placed at distance r from the centre of the shell?

   1. A.$\frac{1}{4\pi {ϵ}_0}\frac{qQ}{R^2}>F>0$ for $r<R$
   2. B.$F=\frac{1}{4\pi {ϵ}_0}\frac{qQ}{r^2}$ for $r>R$
   3. C.$F=\frac{1}{4\pi {ϵ}_0}\frac{qQ}{r^2}$ for all r
   4. D.$F=\frac{1}{4\pi {ϵ}_0}\frac{qQ}{R^2}$ for $r<R$
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   Answer: B

7. Q402020 · 6 Sept 2020 · Shift 2

   Two identical electric point dipoles have dipole moments ${\vec{p}}_1=p\hat{i}$ and ${\vec{p}}_2=-p\hat{i}$ and are held on the x axis at distance '$a$' from each other. When released, they move along the x-axis with the direction of their dipole moments remaining unchanged. If the mass of each dipole is 'm', their speed when they are infinitely far apart is :

   1. A.$\frac{p}{a}\sqrt{\frac{3}{2\pi {ϵ}_{0}ma}}$
   2. B.$\frac{p}{a}\sqrt{\frac{1}{\pi {ϵ}_{0}ma}}$
   3. C.$\frac{p}{a}\sqrt{\frac{1}{2\pi {ϵ}_{0}ma}}$
   4. D.$\frac{p}{a}\sqrt{\frac{2}{\pi {ϵ}_{0}ma}}$
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   Answer: C

8. Q482020 · 6 Sept 2020 · Shift 2· Numerical answer

   In a series LR circuit, power of 400W is dissipated from a source of 250 V, 50 Hz. The power factor of the circuit is 0.8. In order to bring the power factor to unity, a capacitor of value C is added in series to the L and R. Taking the value of C as $\left(\frac{n}{3\pi }\right)\mu \mathrm{F}$, then value of n is ______ .

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   Answer: 400

9. Q302020 · 3 Sept 2020 · Shift 1

   The magnetic field of a plane electromagnetic wave is $\vec{B}=3\times 10^{-8}\sin [200\pi (y+ct)]\hat{i}\mathrm{T}$ where $c=3\times 10^8\mathrm{m}{\mathrm{s}}^{-1}$ is the speed of light. The corresponding electric field is :

   1. A.$\vec{E}=-10^{-6}\sin [200\pi (y+ct)]\hat{k}V/m$
   2. B.$\vec{E}=-9\sin [200\pi (y+ct)]\hat{k}V/m$
   3. C.$\vec{E}=9\sin [200\pi (y+ct)]\hat{k}V/m$
   4. D.$\vec{E}=3\times 10^{-8}\sin [200\pi (y+ct)]\hat{k}$
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   Answer: B

10. Q322020 · 3 Sept 2020 · Shift 1

    A 750 Hz, 20 V (rms) source is connected to a resistance of $100\Omega$, an inductance of $0.1803\mathrm{H}$ and a capacitance of $10\mu \mathrm{F}$ all in series. The time in which the resistance (heat capacity $2\mathrm{J}{/}^{\circ }\mathrm{C}$) will get heated by $10^{\circ }\mathrm{C}$. (assume no loss of heat to the surroudnings) is close to :

    1. A.348 s
    2. B.418 s
    3. C.245 s
    4. D.365 s
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    Answer: A

11. Q362020 · 3 Sept 2020 · Shift 1
    
    1. A.$160\mu \mathrm{C}$
    2. B.$450\mu \mathrm{C}$
    3. C.$590\mu \mathrm{C}$
    4. D.$650\mu \mathrm{C}$
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    Answer: C

12. Q442020 · 3 Sept 2020 · Shift 1

    Two isolated conducting spheres ${\mathrm{S}}_1$ and ${\mathrm{S}}_2$ of radius $\frac{2}{3}R$ and $\frac{1}{3}R$ have $12\mu \mathrm{C}$ and $-3\mu \mathrm{C}$ charges, respectively, and are at a large distance from each other. They are now connected by a conducting wire. A long time after this is done the charges on ${\mathrm{S}}_1$ and ${\mathrm{S}}_2$ are respectively :

    1. A.$4.5\mu \mathrm{C}$ on both
    2. B.$+4.5\mu \mathrm{C}$ and $-4.5\mu \mathrm{C}$
    3. C.$6\mu \mathrm{C}$ and $3\mu \mathrm{C}$
    4. D.$3\mu \mathrm{C}$ and $6\mu \mathrm{C}$
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    Answer: C

13. Q462020 · 3 Sept 2020 · Shift 1· Numerical answer

    A bakelite beaker has volume capacity of 500 cc at $30^{\circ }\mathrm{C}$. When it is partially filled with ${\mathrm{V}}_{\mathrm{m}}$ volume (at $30^{\circ }\mathrm{C}$) of mercury, it is found that the unfilled volume of the beaker remains constant as temperature is varied. If ${\gamma }_{(\mathrm{beaker})}=6\times 10^{-6}{}^{\circ }{\mathrm{C}}^{-1}$ and ${\gamma }_{(\mathrm{mercury})}=1.5\times 10^{-4}{}^{\circ }{\mathrm{C}}^{-1}$, where $\gamma$ is the coefficient of volume expansion, then ${\mathrm{V}}_{\mathrm{m}}$ (in cc) is close to _______.

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    Answer: 20

14. Q382020 · 3 Sept 2020 · Shift 2

    Concentric metallic hollow spheres of radii R and 4R hold charges ${\mathrm{Q}}_1$ and ${\mathrm{Q}}_2$ respectively. Given that surface charge densities of the concentric spheres are equal, the potential difference $\mathrm{V}(\mathrm{R})-\mathrm{V}(4R)$ is :

    1. A.$\frac{3Q_2}{4\pi {\epsilon }_{0}R}$
    2. B.$\frac{3Q_1}{4\pi {\epsilon }_{0}R}$
    3. C.$\frac{3Q_1}{16\pi {\epsilon }_{0}R}$
    4. D.$\frac{Q_2}{4\pi {\epsilon }_{0}R}$
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    Answer: C

15. Q392020 · 3 Sept 2020 · Shift 2

    The electric field of a plane electromagnetic wave propagating along the x direction in vacuum is $\vec{E}=E_0\hat{j}\cos (\omega t-kx)$. The magnetic field $\vec{B}$, at the moment $t=0$ is :

    1. A.$\vec{B}=\frac{E_0}{\sqrt{{\mu }_0{\epsilon }_0}}\cos (kx)\hat{j}$
    2. B.$\vec{B}=\frac{E_0}{\sqrt{{\mu }_0{\epsilon }_0}}\cos (kx)\hat{k}$
    3. C.$\vec{B}=E_0\sqrt{{\mu }_0{\epsilon }_0}\cos (kx)\hat{k}$
    4. D.$\vec{B}=E_0\sqrt{{\mu }_0{\epsilon }_0}\cos (kx)\hat{j}$
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    Answer: C

16. Q262020 · 2 Sept 2020 · Shift 1
    
    1. A.$y=\frac{qEd}{m{V}_0^2}(x-d)$
    2. B.$y=\frac{qEd}{m{V}_0^2}\left(\frac{d}{2}-x\right)$
    3. C.$y=\frac{qEd}{m{V}_0^2}x$
    4. D.$y=\frac{qE{d}^2}{m{V}_0^2}x$
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    Answer: B

17. Q492020 · 2 Sept 2020 · Shift 1· Numerical answer

    A $5\mu \mathrm{F}$ capacitor is charged fully by a $220\mathrm{V}$ supply. It is then disconnected from the supply and is connected in series to another uncharged $2.5\mu \mathrm{F}$ capacitor. If the energy change during the charge redistribution is $\frac{X}{100}\mathrm{J}$ then value of $X$ to the nearest integer is ____.

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    Answer: 4

18. Q262020 · 2 Sept 2020 · Shift 2

    In a plane electromagnetic wave, the directions of electric field and magnetic field are represented by $\hat{k}$ and $2\hat{i}-2\hat{j}$, respectively. What is the unit vector along direction of propagation of the wave?

    1. A.$\frac{1}{\sqrt{5}}(\hat{i}+2\hat{j})$
    2. B.$\frac{1}{\sqrt{5}}(2\hat{i}+\hat{j})$
    3. C.$\frac{1}{\sqrt{2}}(\hat{i}+\hat{j})$
    4. D.$\frac{1}{\sqrt{2}}(\hat{j}+\hat{k})$
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    Answer: C

19. Q362020 · 2 Sept 2020 · Shift 2

    A $10\mu \mathrm{F}$ capacitor is fully charged to a potential difference of 50 V. After removing the source voltage it is connected to an uncharged capacitor in parallel. Now the potential difference across them becomes 20 V. The capacitance of the second capacitor is :

    1. A.$20\mu \mathrm{F}$
    2. B.$15\mu \mathrm{F}$
    3. C.$10\mu \mathrm{F}$
    4. D.$30\mu \mathrm{F}$
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    Answer: B

20. Q382020 · 2 Sept 2020 · Shift 2
    
    1. A.
    2. B.
    3. C.
    4. D.
    Show answer

    Answer: A

21. Q412020 · 2 Sept 2020 · Shift 2
    
    1. A.$\frac{1}{4\pi {\epsilon }_0}\frac{(R+r)}{(R^2+r^2)}Q$
    2. B.$\frac{1}{4\pi {\epsilon }_0}\frac{(R+r)}{2(R^2+r^2)}Q$
    3. C.$\frac{1}{4\pi {\epsilon }_0}\frac{(R+2r)Q}{2(R^2+r^2)}$
    4. D.$\frac{1}{4\pi {\epsilon }_0}\frac{(2R+r)}{(R^2+r^2)}Q$
    Show answer

    Answer: A

22. Q292020 · 9 Jan 2020 · Shift 1
    
    1. A.$\frac{17}{54}$
    2. B.$\frac{18}{54}$
    3. C.$\frac{18}{34}$
    4. D.$\frac{21}{34}$
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    Answer: C

23. Q302020 · 9 Jan 2020 · Shift 1

    The electric fields of two plane electromagnetic plane waves in vacuum are given by $\overrightarrow{E_1}=E_0\hat{j}\cos (\omega t-kx)$ and $\overrightarrow{E_2}=E_0\hat{k}\cos (\omega t-ky)$ At $t=0$, a particle of charge q is at origin with a velocity $\vec{v}=0.8c\hat{j}$ (c is the speed of light in vacuum). The instantaneous force experienced by the particle is :

    1. A.$E_{0}q\left(0.8\hat{i}-\hat{j}+0.4\hat{k}\right)$
    2. B.$E_{0}q\left(-0.8\hat{i}+\hat{j}+\hat{k}\right)$
    3. C.$E_{0}q\left(0.8\hat{i}+\hat{j}+0.2\hat{k}\right)$
    4. D.$E_{0}q\left(0.4\hat{i}-3\hat{j}+0.8\hat{k}\right)$
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    Answer: C

24. Q412020 · 9 Jan 2020 · Shift 1
    
    1. A.(A), (B), (C), (D)
    2. B.(A), (B), (C)
    3. C.(A), (C), (D)
    4. D.(B), (C), (D)
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    Answer: B

25. Q432020 · 9 Jan 2020 · Shift 1

    An electric dipole of moment $\vec{p}=\left(-\hat{i}-3\hat{j}+2\hat{k}\right)\times 10^{-29}\text{ C.m}$ is at the origin $(0,0,0)$. The electric field due to this dipole at $\vec{r}=+\hat{i}+3\hat{j}+5\hat{k}$ (note that $\vec{r}\cdot \vec{p}=0$) is parallel to :

    1. A.$\left(+\hat{i}+3\hat{j}-2\hat{k}\right)$
    2. B.$\left(+\hat{i}-3\hat{j}-2\hat{k}\right)$
    3. C.$\left(-\hat{i}+3\hat{j}-2\hat{k}\right)$
    4. D.$\left(-\hat{i}-3\hat{j}+2\hat{k}\right)$
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    Answer: A