Electrostatics & Capacitors · JEE Main previous year questions

2019 38 questions

1. Q482019 · 12 Apr 2019 · Shift 1

   An electromagnetic wave is represented by the electric field $\vec{E}=E_0\hat{n}\sin \left[\omega t+(6y-8z)\right]$. Taking unit vectors in x, y and z directions to be $\hat{i},\hat{j},\hat{k}$, the direction of propagation $\hat{s}$, is :

   1. A.$\hat{s}=\frac{3\hat{i}-4\hat{j}}{5}$
   2. B.$\hat{s}=\frac{-4\hat{k}+3\hat{j}}{5}$
   3. C.$\hat{s}=\left(\frac{-3\hat{j}+4\hat{k}}{5}\right)$
   4. D.$\hat{s}=\frac{4\hat{j}-3\hat{k}}{5}$
   Show answer

   Answer: C

2. Q312019 · 12 Apr 2019 · Shift 2
   
   1. A.$5.4\mu \text{C}$
   2. B.$9.6\mu \text{C}$
   3. C.$13.4\mu \text{C}$
   4. D.$24\mu \text{C}$
   Show answer

   Answer: D

3. Q342019 · 12 Apr 2019 · Shift 2

   Let a total charge 2Q be distributed in a sphere of radius R, with the charge density given by $\rho (r)=kr$, where r is the distance from the centre. Two charges A and B, of $-Q$ each, are placed on diametrically opposite points, at equal distance, $a$ from the centre. If A and B do not experience any force, then :

   1. A.$a=8^{-1/4}R$
   2. B.$a=2^{-1/4}R$
   3. C.$a=\frac{3R}{2^{1/4}}$
   4. D.$a=\frac{R}{\sqrt{3}}$
   Show answer

   Answer: A

4. Q362019 · 12 Apr 2019 · Shift 2

   A plane electromagnetic wave having a frequency v = 23.9 GHz propagates along the positive z-direction in free space. The peak value of the Electric Field is 60 V/m. Which among the following is the acceptable magnetic field component in the electromagnetic wave ?

   1. A.$\vec{B}=2\times 10^{-7}\sin (1.5\times 10^{2}x+0.5\times 10^{11}t)\hat{j}$
   2. B.$\vec{B}=60\sin (0.5\times 10^{3}x+0.5\times 10^{11}t)\hat{k}$
   3. C.$\vec{B}=2\times 10^{-7}\sin (0.5\times 10^{3}z+1.5\times 10^{11}t)\hat{i}$
   4. D.$\vec{B}=2\times 10^{-7}\sin (0.5\times 10^{3}z-1.5\times 10^{11}t)\hat{i}$
   Show answer

   Answer: D

5. Q312019 · 10 Apr 2019 · Shift 1
   
   1. A.$40\mu \mathrm{F}$ and $10\mu \mathrm{F}$
   2. B.$60\mu \mathrm{F}$ and $40\mu \mathrm{F}$
   3. C.$20\mu \mathrm{F}$ and $30\mu \mathrm{F}$
   4. D.$50\mu \mathrm{F}$ and $30\mu \mathrm{F}$
   Show answer

   Answer: A

6. Q362019 · 10 Apr 2019 · Shift 1

   A cylinder with fixed capacity of 67.2 lit contains helium gas at STP. The amount of heat needed to raise the temperature of the gas by $20^{\circ }\mathrm{C}$ is : [Given that $\mathrm{R}=8.31\mathrm{J}\mathrm{mo}{\mathrm{l}}^{-1}{\mathrm{K}}^{-1}$]

   1. A.374 J
   2. B.700 J
   3. C.748 J
   4. D.350 J
   Show answer

   Answer: C

7. Q412019 · 10 Apr 2019 · Shift 1

   The electric field of a plane electromagnetic wave is given by $\vec{E}=E_0\hat{i}\cos (kz)\cos (\omega t)$ The corresponding magnetic field $\vec{B}$ is then given by

   1. A.$\vec{B}=\frac{E_0}{C}\hat{j}\sin (kz)\sin (\omega t)$
   2. B.$\vec{B}=\frac{E_0}{C}\hat{j}\sin (kz)\cos (\omega t)$
   3. C.$\vec{B}=\frac{E_0}{C}\hat{j}\cos (kz)\sin (\omega t)$
   4. D.$\vec{B}=\frac{E_0}{C}\hat{k}\sin (kz)\cos (\omega t)$
   Show answer

   Answer: A

8. Q512019 · 10 Apr 2019 · Shift 1

   A uniformly charged ring of radius 3a and total charge q is placed in xy-plane centred at origin. A point charge q is moving towards the ring along the z-axis and has speed u at z = 4a. The minimum value of u such that it crosses the origin is :

   1. A.$\sqrt{\frac{2}{m}}{\left(\frac{2}{15}\frac{q^2}{4\pi {\epsilon }_{0}a}\right)}^{1/2}$
   2. B.$\sqrt{\frac{2}{m}}{\left(\frac{1}{15}\frac{q^2}{4\pi {\epsilon }_{0}a}\right)}^{1/2}$
   3. C.$\sqrt{\frac{2}{m}}{\left(\frac{1}{5}\frac{q^2}{4\pi {\epsilon }_{0}a}\right)}^{1/2}$
   4. D.$\sqrt{\frac{2}{m}}{\left(\frac{4}{15}\frac{q^2}{4\pi {\epsilon }_{0}a}\right)}^{1/2}$
   Show answer

   Answer: A

9. Q322019 · 10 Apr 2019 · Shift 2

   In free space, a particle A of charge $1\mu \mathrm{C}$ is held fixed at a point P. Another particle B of the same charge and mass $4\mu \mathrm{g}$ is kept at a distance of 1 mm from P. If B is released, then its velocity at a distance of 9 mm from P is : $\left[\mathrm{Take}\frac{1}{4\pi {ϵ}_0}=9\times 10^9\mathrm{N}{\mathrm{m}}^2{\mathrm{C}}^{-2}\right]$

   1. A.1.0 m/s
   2. B.$6.32\times 10^{4}m/s$
   3. C.$2.0\times 10^{3}m/s$
   4. D.$1.5\times 10^{2}m/s$
   Show answer

   Answer: B

10. Q402019 · 10 Apr 2019 · Shift 2

    A square loop is carrying a steady current I and the magnitude of its magnetic dipole moment is m. if this square loop is changed to a circular loop and it carries the same current, the magnitude of the magnetic dipole moment of circular loop will be:

    1. A.$\frac{m}{\pi }$
    2. B.$\frac{3m}{\pi }$
    3. C.$\frac{2m}{\pi }$
    4. D.$\frac{4m}{\pi }$
    Show answer

    Answer: D

11. Q532019 · 10 Apr 2019 · Shift 2
    
    1. A.$2\pi \sqrt{\frac{L}{\sqrt{g^2-\frac{q^2{E}^2}{m^2}}}}$
    2. B.$2\pi \sqrt{\frac{L}{\left(g+\frac{qE}{m}\right)}}$
    3. C.$2\pi \sqrt{\frac{L}{\sqrt{g^2+\frac{q^2{E}^2}{m^2}}}}$
    4. D.$2\pi \sqrt{\frac{L}{\left(g-\frac{qE}{m}\right)}}$
    Show answer

    Answer: C

12. Q372019 · 9 Apr 2019 · Shift 1
    
    1. A.$200\mu \mathrm{C}$
    2. B.$2\mu \mathrm{C}$
    3. C.$10\mu \mathrm{C}$
    4. D.$60\mu \mathrm{C}$
    Show answer

    Answer: A

13. Q442019 · 9 Apr 2019 · Shift 1

    The electric field of light wave is given as $$\vec{E}=10^{-3}\cos \left(\frac{2\pi x}{5\times 10^{-7}}-2\pi \times 6\times 10^{14}t\right)\hat{x}\frac{\mathrm{N}}{\mathrm{C}}$$ This light falls on a metal plate of work function 2eV. The stopping potential of the photoelectrons is : Given, E (in eV) = 12375/$\lambda$(inÅ)

    1. A.2.48 V
    2. B.0.48 V
    3. C.0.72 V
    4. D.2.0 V
    Show answer

    Answer: B

14. Q462019 · 9 Apr 2019 · Shift 1

    A capacitor with capacitance $5\mu \mathrm{F}$ is charged to $5\mu \mathrm{C}$. If the plates are pulled apart to reduce the capacitance to $2\mu \mathrm{F}$, how much work is done ?

    1. A.$2.16\times 10^{-6}\mathrm{J}$
    2. B.$2.55\times 10^{-6}\mathrm{J}$
    3. C.$3.75\times 10^{-6}\mathrm{J}$
    4. D.$6.25\times 10^{-6}\mathrm{J}$
    Show answer

    Answer: C

15. Q462019 · 9 Apr 2019 · Shift 2

    Four point charges $-q$, $+q$, $+q$ and $-q$ are placed on y-axis at $y=-2d$, $y=-d$, $y=+d$ and $y=+2d$, respectively. The magnitude of the electric field E at a point on the x-axis at $x=D$, with D >> d, will behave as :-

    1. A.$E\propto \frac{1}{D^3}$
    2. B.$E\propto \frac{1}{D}$
    3. C.$E\propto \frac{1}{D^4}$
    4. D.$E\propto \frac{1}{D^2}$
    Show answer

    Answer: C

16. Q562019 · 9 Apr 2019 · Shift 2

    The parallel combination of two air filled parallel plate capacitors of capacitance C and nC is connected to a battery of voltage, V. When the capacitors are fully charged, the battery is removed and after that a dielectric material of dielectric constant K is placed between the two plates of the first capacitor. The new potential difference of the combined system is :-

    1. A.V
    2. B.$\frac{V}{K+n}$
    3. C.$\frac{(n+1)V}{K+n}$
    4. D.$\frac{nV}{K+n}$
    Show answer

    Answer: C

17. Q352019 · 8 Apr 2019 · Shift 2

    An electric dipole is formed by two equal and opposite charges q with separation d. The charges have same mass m. It is kept in a uniform electric field E. If it is slightly rotated from its equilibrium orientation, then its angular frequency $\omega$ is :-

    1. A.$\sqrt{\frac{qE}{md}}$
    2. B.$\sqrt{\frac{qE}{2md}}$
    3. C.$\sqrt{\frac{qE}{-2md}}$
    4. D.$\sqrt{\frac{2qE}{md}}$
    Show answer

    Answer: D

18. Q372019 · 8 Apr 2019 · Shift 2

    The magnetic field of an electromagnetic wave is given by :- $$\vec{B}=1.6\times 10^{-6}\cos (2\times 10^{7}z+6\times 10^{15}t)(2\hat{i}+\hat{j})\frac{\mathrm{Wb}}{{\mathrm{m}}^2}$$ The associated electric field will be :-

    1. A.$\vec{E}=4.8\times 10^2\cos (2\times 10^{7}z-6\times 10^{15}t)(-2\hat{i}+\hat{j})\frac{\mathrm{V}}{\mathrm{m}}$
    2. B.$\vec{E}=4.8\times 10^2\cos (2\times 10^{7}z-6\times 10^{15}t)(2\hat{i}+\hat{j})\frac{\mathrm{V}}{\mathrm{m}}$
    3. C.$\vec{E}=4.8\times 10^2\cos (2\times 10^{7}z+6\times 10^{15}t)(\hat{i}-2\hat{j})\frac{\mathrm{V}}{\mathrm{m}}$
    4. D.$\vec{E}=4.8\times 10^2\cos (2\times 10^{7}z+6\times 10^{15}t)(-\hat{i}+2\hat{j})\frac{\mathrm{V}}{\mathrm{m}}$
    Show answer

    Answer: D

19. Q422019 · 8 Apr 2019 · Shift 2

    A positive point charge is released from rest at a distance $r_0$ from a positive line charge with uniform density. The speed (v) of the point charge, as a function of instantaneous distance r from line charge, is proportional to :-

    1. A.$v\propto \left(\frac{r}{r_0}\right)$
    2. B.$v\propto \ln \left(\frac{r}{r_0}\right)$
    3. C.$v\propto e^{+r/r_0}$
    4. D.$v\propto \sqrt{\ln \left(\frac{r}{r_0}\right)}$
    Show answer

    Answer: D

20. Q432019 · 8 Apr 2019 · Shift 2

    The electric field in a region is given by $\vec{E}=(Ax+B)\hat{i}$, where E is in $\mathrm{N}{\mathrm{C}}^{-1}$ and x is in metres. The values of constants are A = 20 SI unit and B = 10 SI unit. If the potential at x = 1 is $V_1$ and that at x = –5 is $V_2$, then $V_1-V_2$ is :-

    1. A.−520 V
    2. B.180 V
    3. C.−48 V
    4. D.320 V
    Show answer

    Answer: B

21. Q442019 · 8 Apr 2019 · Shift 2

    A parallel plate capacitor has 1μF capacitance. One of its two plates is given +2μC charge and the other plate, +4μC charge. The potential difference developed across the capacitor is:-

    1. A.1V
    2. B.5V
    3. C.2V
    4. D.3V
    Show answer

    Answer: A

22. Q552019 · 8 Apr 2019 · Shift 2
    
    1. A.$\left(\frac{{\mu }_0}{4\pi }\right)\frac{2M}{(d/2{)}^3}\times qv$
    2. B.$\left(\frac{{\mu }_0}{4\pi }\right)\frac{M}{(d/2{)}^3}\times qv$
    3. C.$\sqrt{2}\left(\frac{{\mu }_0}{4\pi }\right)\frac{M}{(d/2{)}^3}\times qv$
    4. D.0
    Show answer

    Answer: D

23. Q362019 · 12 Jan 2019 · Shift 1

    A light wave is incident normally on a glass slab of refractive index 1.5. If 4 % of light gets reflected and the amplitude of the electric field of the incident light is 30 V/m, then the amplitude of the electric field for the wave propagating in the glass medium will be :

    1. A.6 V/m
    2. B.10 V/m
    3. C.30 V/m
    4. D.24 V/m
    Show answer

    Answer: D

24. Q372019 · 12 Jan 2019 · Shift 1
    
    1. A.$2ql\hat{j}$
    2. B.$(ql)\frac{\hat{i}+\hat{j}}{\sqrt{2}}$
    3. C.$\sqrt{3}ql\frac{\hat{j}-\hat{i}}{\sqrt{2}}$
    4. D.$-\sqrt{3}ql\hat{j}$
    Show answer

    Answer: D

25. Q472019 · 12 Jan 2019 · Shift 1
    
    1. A.$\frac{1}{8}\frac{Q^2}{C}$
    2. B.$\frac{5}{8}\frac{Q^2}{C}$
    3. C.$\frac{3}{4}\frac{Q^2}{C}$
    4. D.$\frac{3}{8}\frac{Q^2}{C}$
    Show answer

    Answer: D