Electrostatics & Capacitors · JEE Main previous year questions

2023 63 questions

1. Q382023 · 13 Apr 2023 · Shift 1

   The source of time varying magnetic field may be (A) a permanent magnet (B) an electric field changing linearly with time (C) direct current (D) a decelerating charge particle (E) an antenna fed with a digital signal Choose the correct answer from the options given below:

   1. A.(D) only
   2. B.(A) only
   3. C.(B) and (D) only
   4. D.(C) and (E) only
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   Answer: A

2. Q392023 · 13 Apr 2023 · Shift 1

   Two charges each of magnitude $0.01\text{ C}$ and separated by a distance of $0.4\text{ mm}$ constitute an electric dipole. If the dipole is placed in an uniform electric field '$\vec{E}$' of $10\text{ dyne/C}$ making $30^{\circ }$ angle with $\vec{E}$, the magnitude of torque acting on dipole is:

   1. A.$4.0\times 10^{-10}\text{ Nm}$
   2. B.$1.5\times 10^{-9}\text{ Nm}$
   3. C.$1.0\times 10^{-8}\text{ Nm}$
   4. D.$2.0\times 10^{-10}\text{ Nm}$
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   Answer: D

3. Q572023 · 13 Apr 2023 · Shift 1· Numerical answer

   A thin infinite sheet charge and an infinite line charge of respective charge densities $+\sigma$ and $+\lambda$ are placed parallel at $5\text{ m}$ distance from each other. Points 'P' and 'Q' are at $\frac{3}{\pi }\text{ m}$ and $\frac{4}{\pi }\text{ m}$ perpendicular distances from line charge towards sheet charge, respectively. '${\mathrm{E}}_P$' and '${\mathrm{E}}_Q$' are the magnitudes of resultant electric field intensities at point 'P' and 'Q', respectively. If $\frac{{\mathrm{E}}_P}{{\mathrm{E}}_Q}=\frac{4}{a}$ for $2|\sigma |=|\lambda |$, then the value of $a$ is ___________.

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   Answer: 6

4. Q382023 · 13 Apr 2023 · Shift 2

   In an electromagnetic wave, at an instant and at particular position, the electric field is along the negative $z$-axis and magnetic field is along the positive $x$-axis. Then the direction of propagation of electromagnetic wave is:

   1. A.at $45^{\circ }$ angle from positive y-axis
   2. B.positive $y$-axis
   3. C.negative $y$-axis
   4. D.positive z-axis
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   Answer: C

5. Q392023 · 13 Apr 2023 · Shift 2
   
   1. A.$10.3\mu \mathrm{C}$
   2. B.$7.2\mu \mathrm{C}$
   3. C.$4.8\mu \mathrm{C}$
   4. D.$12\mu \mathrm{C}$
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   Answer: B

6. Q432023 · 13 Apr 2023 · Shift 2

   A $10\mu \mathrm{C}$ charge is divided into two parts and placed at $1\text{ cm}$ distance so that the repulsive force between them is maximum. The charges of the two parts are:

   1. A.$9\mu \mathrm{C},1\mu \mathrm{C}$
   2. B.$5\mu \mathrm{C},5\mu \mathrm{C}$
   3. C.$8\mu \mathrm{C},2\mu \mathrm{C}$
   4. D.$7\mu \mathrm{C},3\mu \mathrm{C}$
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   Answer: B

7. Q442023 · 13 Apr 2023 · Shift 2

   Given below are two statements: Statement I : An AC circuit undergoes electrical resonance if it contains either a capacitor or an inductor. Statement II : An AC circuit containing a pure capacitor or a pure inductor consumes high power due to its non-zero power factor. In the light of above statements, choose the correct answer from the options given below:

   1. A.Both Statement I and Statement II are false
   2. B.Statement I is true but statement II is false
   3. C.Statement I is false but statement II is true
   4. D.Both Statement I and Statement II are true
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   Answer: A

8. Q512023 · 13 Apr 2023 · Shift 2· Numerical answer
   
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   Answer: 5440

9. Q582023 · 13 Apr 2023 · Shift 2· Numerical answer
   
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   Answer: 75

10. Q402023 · 12 Apr 2023 · Shift 1

    Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A : If an electric dipole of dipole moment $30\times 10^{-5}\text{ C m}$ is enclosed by a closed surface, the net flux coming out of the surface will be zero. Reason R : Electric dipole consists of two equal and opposite charges. In the light of the above statements, choose the correct answer from the options given below.

    1. A.A is true but R is false
    2. B.A is false but R is true
    3. C.Both A and R are true but R is NOT the correct explanation of A
    4. D.Both A and R are true and R is the correct explanation of A
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    Answer: D

11. Q412023 · 12 Apr 2023 · Shift 1

    Given below are two statements: Statement I : The diamagnetic property depends on temperature. Statement II : The induced magnetic dipole moment in a diamagnetic sample is always opposite to the magnetizing field. In the light of given statements, choose the correct answer from the options given below.

    1. A.Statement I is incorrect but Statement II is true.
    2. B.Statement I is correct but Statement II is false.
    3. C.Both Statement I and Statement II are False.
    4. D.Both Statement I and Statement II are true.
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    Answer: A

12. Q402023 · 11 Apr 2023 · Shift 1

    A parallel plate capacitor of capacitance $2\mathrm{F}$ is charged to a potential $V$, The energy stored in the capacitor is $E_1$. The capacitor is now connected to another uncharged identical capacitor in parallel combination. The energy stored in the combination is $E_2$. The ratio $E_2/E_1$ is :

    1. A.1 : 2
    2. B.2 : 3
    3. C.2 : 1
    4. D.1 : 4
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    Answer: A

13. Q412023 · 11 Apr 2023 · Shift 1

    The electric field in an electromagnetic wave is given as $$\vec{E}=20\sin \omega \left(t-\frac{x}{c}\right)\vec{\mathrm{j}}\mathrm{N}{\mathrm{C}}^{-1}$$ where $\omega$ and $c$ are angular frequency and velocity of electromagnetic wave respectively. The energy contained in a volume of $5\times 10^{-4}{\mathrm{m}}^3$ will be (Given ${\epsilon }_0=8.85\times 10^{-12}{\mathrm{C}}^2/N{\mathrm{m}}^2$ )

    1. A.$17.7\times 10^{-13}\mathrm{J}$
    2. B.$28.5\times 10^{-13}\mathrm{J}$
    3. C.$8.85\times 10^{-13}\mathrm{J}$
    4. D.$88.5\times 10^{-13}\mathrm{J}$
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    Answer: C

14. Q382023 · 11 Apr 2023 · Shift 2

    A capacitor of capacitance $\mathrm{C}$ is charged to a potential $\mathrm{V}$. The flux of the electric field through a closed surface enclosing the positive plate of the capacitor is :

    1. A.Zero
    2. B.$\frac{\mathrm{CV}}{{\epsilon }_0}$
    3. C.$\frac{\mathrm{CV}}{2{\epsilon }_0}$
    4. D.$\frac{2\mathrm{CV}}{{\epsilon }_0}$
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    Answer: B

15. Q582023 · 11 Apr 2023 · Shift 2· Numerical answer
    
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    Answer: 4

16. Q352023 · 10 Apr 2023 · Shift 1
    
    1. A.$\frac{C}{2}$
    2. B.$4C$
    3. C.$\frac{5}{3}C$
    4. D.$2C$
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    Answer: D

17. Q452023 · 10 Apr 2023 · Shift 1

    Given below are two statements: Statement I : Maximum power is dissipated in a circuit containing an inductor, a capacitor and a resistor connected in series with an AC source, when resonance occurs Statement II : Maximum power is dissipated in a circuit containing pure resistor due to zero phase difference between current and voltage. In the light of the above statements, choose the correct answer from the options given below:

    1. A.Statement I is false but Statement II is true
    2. B.Both Statement I and Statement II are false
    3. C.Statement I is true but Statement II is false
    4. D.Both Statement I and Statement II are true
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    Answer: D

18. Q562023 · 10 Apr 2023 · Shift 1· Numerical answer

    Three concentric spherical metallic shells X, Y and Z of radius a, b and c respectively [$a<b<c$] have surface charge densities $\sigma ,-\sigma$ and $\sigma$ respectively. The shells X and Z are at same potential. If the radii of X & Y are 2 cm and 3 cm, respectively. The radius of shell Z is _________ cm.

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    Answer: 5

19. Q342023 · 10 Apr 2023 · Shift 2

    In a metallic conductor, under the effect of applied electric field, the free electrons of the conductor

    1. A.move in the straight line paths in the same direction
    2. B.move with the uniform velocity throughout from lower potential to higher potential
    3. C.drift from higher potential to lower potential.
    4. D.move in the curved paths from lower potential to higher potential
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    Answer: D

20. Q402023 · 10 Apr 2023 · Shift 2

    The amplitude of magnetic field in an electromagnetic wave propagating along y-axis is $6.0\times 10^{-7}\text{ T}$. The maximum value of electric field in the electromagnetic wave is

    1. A.$6.0\times 10^{-7}{\text{ Vm}}^{-1}$
    2. B.$5\times 10^{14}{\text{ Vm}}^{-1}$
    3. C.$180{\text{ Vm}}^{-1}$
    4. D.$2\times 10^{15}{\text{ Vm}}^{-1}$
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    Answer: C

21. Q482023 · 10 Apr 2023 · Shift 2

    The distance between two plates of a capacitor is d and its capacitance is $C_1$, when air is the medium between the plates. If a metal sheet of thickness $\frac{2d}{3}$ and of the same area as plate is introduced between the plates, the capacitance of the capacitor becomes $C_2$. The ratio $\frac{C_2}{C_1}$ is

    1. A.$1:1$
    2. B.$3:1$
    3. C.$2:1$
    4. D.$4:1$
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    Answer: B

22. Q562023 · 10 Apr 2023 · Shift 2· Numerical answer
    
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    Answer: 8

23. Q362023 · 8 Apr 2023 · Shift 1
    
    1. A.
    2. B.
    3. C.
    4. D.
    Show answer

    Answer: D

24. Q562023 · 8 Apr 2023 · Shift 1· Numerical answer

    An electric dipole of dipole moment $6.0\times 10^{-6}\text{ Cm}$ is placed in a uniform electric field of $1.5\times 10^3{\text{ NC}}^{-1}$ in such a way that dipole moment is along electric field. The work done in rotating dipole by $180^{\circ }$ in this field will be ___________ $\text{mJ}$.

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    Answer: 18

25. Q592023 · 8 Apr 2023 · Shift 1· Numerical answer

    An oscillating LC circuit consists of a $75\text{ mH}$ inductor and a $1.2\mu \text{F}$ capacitor. If the maximum charge to the capacitor is $2.7\mu \text{C}$. The maximum current in the circuit will be ___________ $\text{mA}$

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    Answer: 9