Electrostatics & Capacitors · JEE Main previous year questions

2021 35 questions

1. 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

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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