Electrostatics & Capacitors · JEE Main previous year questions

2021 35 questions

1. Q382021 · 25 Jul 2021 · Shift 2

   If $q_f$ is the free charge on the capacitor plates and $q_b$ is the bound charge on the dielectric slab of dielectric constant k placed between the capacitor plates, then bound charge $q_b$ an be expressed as :

   1. A.$q_b=q_f\left(1-\frac{1}{\sqrt{k}}\right)$
   2. B.$q_b=q_f\left(1-\frac{1}{k}\right)$
   3. C.$q_b=q_f\left(1+\frac{1}{\sqrt{k}}\right)$
   4. D.$q_b=q_f\left(1+\frac{1}{k}\right)$
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   Answer: B

2. Q402021 · 25 Jul 2021 · Shift 2
   
   1. A.$\frac{3}{8}$
   2. B.$\frac{3}{2}$
   3. C.$\frac{2}{3}$
   4. D.$\frac{4}{3}$
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   Answer: C

3. Q382021 · 22 Jul 2021 · Shift 2

   An electric dipole is placed on x-axis in proximity to a line charge of linear charge density $3.0\times 10^{-6}\text{ C/m}$. Line charge is placed on z-axis and positive and negative charge of dipole is at a distance of $10\text{ mm}$ and $12\text{ mm}$ from the origin respectively. If total force of $4\text{N}$ is exerted on the dipole, find out the amount of positive or negative charge of the dipole.

   1. A.$0.485\text{ mC}$
   2. B.$815.1\text{ nC}$
   3. C.$8.8\mu \text{C}$
   4. D.$4.44\mu \text{C}$
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   Answer: D

4. Q552021 · 22 Jul 2021 · Shift 2· Numerical answer

   The total charge enclosed in an incremental volume of $2\times 10^{-9}{\text{ m}}^3$ located at the origin is ________ nC, if electric flux density of its field is found as $\text{D}=e^{-x}\sin y\hat{i}-e^{-x}\cos y\hat{j}+2z\hat{k}{\text{C/m}}^2$

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   Answer: 4

5. Q332021 · 20 Jul 2021 · Shift 1

   A current of $5\text{ A}$ is passing through a non-linear magnesium wire of cross-section $0.04{\text{ m}}^2$. At every point the direction of current density is at an angle of $60^{\circ }$ with the unit vector of area of cross-section. The magnitude of electric field at every point of the conductor is : (Resistivity of magnesium $\rho =44\times 10^{-8}\Omega \text{m}$)

   1. A.$11\times 10^{-5}\text{ V/m}$
   2. B.$11\times 10^{-3}\text{ V/m}$
   3. C.$11\times 10^{-7}\text{ V/m}$
   4. D.$11\times 10^{-2}\text{ V/m}$
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   Answer: A

6. Q382021 · 20 Jul 2021 · Shift 1

   A certain charge Q is divided into two parts q and $(Q-q)$. How should the charges Q and q be divided so that q and $(Q-q)$ placed at a certain distance apart experience maximum electrostatic repulsion?

   1. A.$Q=2q$
   2. B.$Q=4q$
   3. C.$Q=3q$
   4. D.$Q=\frac{q}{2}$
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   Answer: A

7. Q462021 · 20 Jul 2021 · Shift 1

   AC voltage $V(t)=20\sin \omega t$ of frequency $50\text{ Hz}$ is applied to a parallel plate capacitor. The separation between the plates is $2\text{ mm}$ and the area is $1{\text{ m}}^2$. The amplitude of the oscillating displacement current for the applied AC voltage is ________. [Take ${\epsilon }_0=8.85\times 10^{-12}\text{ F/m}$]

   1. A.$55.58\mu \text{A}$
   2. B.$21.14\mu \text{A}$
   3. C.$27.79\mu \text{A}$
   4. D.$83.37\mu \text{A}$
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   Answer: C

8. Q512021 · 20 Jul 2021 · Shift 1· Numerical answer
   
   Show answer

   Answer: 1

9. Q312021 · 18 Mar 2021 · Shift 1

   An oil drop of radius $2\text{ mm}$ with a density $3{\text{g cm}}^{-3}$ is held stationary under a constant electric field $3.55\times 10^5{\text{ V m}}^{-1}$ in the Millikan's oil drop experiment. What is the number of excess electrons that the oil drop will possess? (consider $\mathrm{g}=9.81{\text{ m/s}}^2$)

   1. A.$48.8\times 10^{11}$
   2. B.$1.73\times 10^{10}$
   3. C.$17.3\times 10^{10}$
   4. D.$1.73\times 10^{12}$
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   Answer: B

10. Q322021 · 18 Mar 2021 · Shift 1

    Imagine that the electron in a hydrogen atom is replaced by a muon $(\mu )$. The mass of muon particle is 207 times that of an electron and charge is equal to the charge of an electron. The ionization potential of this hydrogen atom will be :

    1. A.$13.6\text{ eV}$
    2. B.$2815.2\text{ eV}$
    3. C.$331.2\text{ eV}$
    4. D.$27.2\text{ eV}$
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    Answer: B

11. Q522021 · 18 Mar 2021 · Shift 1· Numerical answer
    
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    Answer: 2

12. Q562021 · 18 Mar 2021 · Shift 1· Numerical answer

    A parallel plate capacitor has plate area $100{\text{ m}}^2$ and plate separation of 10 m. The space between the plates is filled up to a thickness 5 m with a material of dielectric constant of 10. The resultant capacitance of the system is 'x' pF. The value of ${\epsilon }_0=8.85\times 10^{-12}{\text{ F.m}}^{-1}$. The value of 'x' to the nearest integer is _______.

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    Answer: 161

13. Q312021 · 18 Mar 2021 · Shift 2

    A plane electromagnetic wave propagating along y-direction can have the following pair of electric field $(\vec{E})$ and magnetic field $(\vec{B})$ components.

    1. A.$E_x,B_z$ or $E_z,B_x$
    2. B.$E_x,B_y$ or $E_y,B_x$
    3. C.$E_y,B_y$ or $E_z,B_z$
    4. D.$E_y,B_x$ or $E_x,B_y$
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    Answer: A

14. Q392021 · 16 Mar 2021 · Shift 1

    For changing the capacitance of a given parallel plate capacitor, a dielectric material of dielectric constant K is used, which has the same area as the plates of the capacitor. The thickness of the dielectric slab is $\frac{3}{4}\mathrm{d}$, where 'd' is the separation between the plates of parallel plate capacitor. The new capacitance (${\mathrm{C}}^{\prime }$) in terms of original capacitance (${\mathrm{C}}_0$) is given by the following relation :

    1. A.$C^{\prime }=\frac{3+K}{4K}{C}_0$
    2. B.$C^{\prime }=\frac{4+K}{3}{C}_0$
    3. C.$C^{\prime }=\frac{4K}{K+3}{C}_0$
    4. D.$C^{\prime }=\frac{4}{3+K}{C}_0$
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    Answer: C

15. Q402021 · 16 Mar 2021 · Shift 1

    A plane electromagnetic wave of frequency 500 MHz is travelling in vacuum along y-direction. At a particular point in space and time, $\vec{B}=8.0\times 10^{-8}\hat{z}\mathrm{T}$. The value of electric field at this point is : (speed of light = $3\times 10^8\mathrm{m}{\mathrm{s}}^{-1}$) $\hat{x},\hat{y},\hat{z}$ are unit vectors along x, y and z directions.

    1. A.$2.6\hat{x}V/m$
    2. B.$-24\hat{x}V/m$
    3. C.$24\hat{x}V/m$
    4. D.$-2.6\hat{y}V/m$
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    Answer: B

16. Q312021 · 26 Feb 2021 · Shift 1

    Consider the combination of 2 capacitors $C_1$ and $C_2$ with $C_2>C_1$, when connected in parallel, the equivalent capacitance is $\frac{15}{4}$ times the equivalent capacitance of the same connected in series. Calculate the ratio of capacitors, $\frac{C_2}{C_1}$.

    1. A.$\frac{15}{11}$
    2. B.No Solutions
    3. C.$\frac{29}{15}$
    4. D.$\frac{15}{4}$
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    Answer: B

17. Q432021 · 26 Feb 2021 · Shift 1
    
    1. A.$\frac{Q}{4\pi {\epsilon }_0{L}^2}$
    2. B.$\frac{Q}{3\pi {\epsilon }_0{L}^2}$
    3. C.$\frac{Q}{2\sqrt{3}\pi {\epsilon }_0{L}^2}$
    4. D.$\frac{\sqrt{3}Q}{4\pi {\epsilon }_0{L}^2}$
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    Answer: C

18. Q562021 · 26 Feb 2021 · Shift 1· Numerical answer

    A radiation is emitted by 1000W bulb and it generates an electric field and magnetic field at P, placed at a distance of 2m. The efficiency of the bulb is 1.25%. The value of peak electric field at P is $x\times 10^{-1}V/m$. Value of x is _________. (Rounded off to the nearest integer) [Take ${\epsilon }_0=8.85\times 10^{-12}{\mathrm{C}}^2{\mathrm{N}}^{-1}{\mathrm{m}}^{-2},c=3\times 10^8\mathrm{m}{\mathrm{s}}^{-1}$]

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    Answer: 137

19. Q352021 · 26 Feb 2021 · Shift 2

    Given below are two statements: Statement I : An electric dipole is placed at the center of a hollow sphere. The flux of the electric field through the sphere is zero but the electric field is not zero anywhere in the sphere. Statement II : If R is the radius of a solid metallic sphere and Q be the total charge on it. The electric field at any point on the spherical surface of radius r (< R) is zero but the electric flux passing through this closed spherical surface of radius r is not zero. 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 false but Statement II is true
    3. C.Statement I is true but Statement II is false
    4. D.Both Statement I and Statement II are false
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    Answer: C

20. Q442021 · 26 Feb 2021 · Shift 2
    
    1. A.0.46 s
    2. B.0.92 s
    3. C.1.3 s
    4. D.2.3 s
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    Answer: C

21. Q512021 · 26 Feb 2021 · Shift 2· Numerical answer

    1 mole of rigid diatomic gas performs a work of $\frac{Q}{5}$ when heat Q is supplied to it. The molar heat capacity of the gas during this transformation is $\frac{xR}{8}$. The value of x is _________. [R = universal gas constant]

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    Answer: 25

22. Q322021 · 25 Feb 2021 · Shift 2

    An electron with kinetic energy $K_1$ enters between parallel plates of a capacitor at an angle '$\alpha$' with the plates. It leaves the plates at angle '$\beta$' with kinetic energy $K_2$. Then the ratio of kinetic energies $K_1:K_2$ will be :

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

23. Q392021 · 25 Feb 2021 · Shift 2
    
    1. A.$\frac{q}{24{ϵ}_0}$
    2. B.$\frac{q}{48{ϵ}_0}$
    3. C.$\frac{q}{4{ϵ}_0}$
    4. D.$\frac{q}{8{ϵ}_0}$
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    Answer: A

24. Q542021 · 25 Feb 2021 · Shift 2· Numerical answer

    The peak electric field produced by the radiation coming from the 8W bulb at a distance of 10 m is $\frac{x}{10}\sqrt{\frac{{\mu }_{0}c}{\pi }}\frac{V}{m}$. The efficiency of the bulb is 10% and it is a point source. The value of x is ______ .

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    Answer: 2

25. Q572021 · 25 Feb 2021 · Shift 2· Numerical answer

    Two small spheres each of mass 10 mg are suspended from a point by threads 0.5 m long. They are equally charged and repel each other to a distance of 0.20 m. The charge on each of the sphere is $\frac{a}{21}\times 10^{-8}\text{ C}$. The value of 'a' will be ______ . [Given $g=10\mathrm{m}{\mathrm{s}}^{-2}$]

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    Answer: 20