Electrostatics & Capacitors · JEE Main previous year questions

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2022 56 questions

Q402022 · 30 Jun 2022 · Shift 1
1. A. $\frac{C _{o}}{2} (1 + ε_{r})$
2. B. $C_{o} + ε_{r}$
3. C. $\frac{C _{o} ε _{r}}{2}$
4. D. $C_{o} (1 + ε_{r})$
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Answer: A
Q432022 · 30 Jun 2022 · Shift 1
An expression for oscillating electric field in a plane electromagnetic wave is given as $E_{z} = 300 sin (5 π \times 1 0^{3} x - 3 π \times 1 0^{11} t) Vm^{- 1}$ Then, the value of magnetic field amplitude will be : (Given : speed of light in Vacuum $c = 3 \times 1 0^{8} ms^{- 1}$ )
1. A. $1 \times 1 0^{- 6} T$
2. B. $5 \times 1 0^{- 6} T$
3. C. $18 \times 1 0^{9} T$
4. D. $21 \times 1 0^{9} T$
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Answer: B
Q552022 · 30 Jun 2022 · Shift 1· Numerical answer
A series LCR circuit with $R = \frac{250}{11} Ω$ and $X_{L} = \frac{70}{11} Ω$ is connected across a $220 V$ , $50 Hz$ supply. The value of capacitance needed to maximize the average power of the circuit will be ___________ $μ F$ . (Take : $π = \frac{22}{7}$ )
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Answer: 500
Q402022 · 28 Jun 2022 · Shift 2
Two point charges A and B of magnitude $+ 8 \times 1 0^{- 6} C$ and $- 8 \times 1 0^{- 6} C$ respectively are placed at a distance d apart. The electric field at the middle point O between the charges is $6.4 \times 1 0^{4} N C^{- 1}$ . The distance 'd' between the point charges A and B is :
1. A. $2.0 m$
2. B. $3.0 m$
3. C. $1.0 m$
4. D. $4.0 m$
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Answer: B
Q452022 · 28 Jun 2022 · Shift 2
An EM wave propagating in x-direction has a wavelength of $8 mm$ . The electric field vibrating y-direction has maximum magnitude of $60 V m^{- 1}$ . Choose the correct equations for electric and magnetic fields if the EM wave is propagating in vacuum :
1. A. $E_{y} = 60 sin [\frac{π}{4} \times 1 0^{3} (x - 3 \times 1 0^{8} t)] \hat{j} V m^{- 1}$ , $B_{z} = 2 sin [\frac{π}{4} \times 1 0^{3} (x - 3 \times 1 0^{8} t)] \hat{k} T$
2. B. $E_{y} = 60 sin [\frac{π}{4} \times 1 0^{3} (x - 3 \times 1 0^{8} t)] \hat{j} V m^{- 1}$ , $B_{z} = 2 \times 1 0^{- 7} sin [\frac{π}{4} \times 1 0^{3} (x - 3 \times 1 0^{8} t)] \hat{k} T$
3. C. $E_{y} = 2 \times 1 0^{- 7} sin [\frac{π}{4} \times 1 0^{3} (x - 3 \times 1 0^{8} t)] \hat{j} V m^{- 1}$ , $B_{z} = 60 sin [\frac{π}{4} \times 1 0^{3} (x - 3 \times 1 0^{8} t)] \hat{k} T$
4. D. $E_{y} = 2 \times 1 0^{- 7} sin [\frac{π}{4} \times 1 0^{4} (x - 4 \times 1 0^{8} t)] \hat{j} V m^{- 1}$ , $B_{z} = 60 sin [\frac{π}{4} \times 1 0^{4} (x - 4 \times 1 0^{8} t)] \hat{k} T$
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Answer: B
Q562022 · 28 Jun 2022 · Shift 2· Numerical answer
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Answer: 100
Q442022 · 27 Jun 2022 · Shift 1
A force of 10 N acts on a charged particle placed between two plates of a charged capacitor. If one plate of capacitor is removed, then the force acting on that particle will be.
1. A.5 N
2. B.10 N
3. C.20 N
4. D.Zero
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Answer: A
Q552022 · 27 Jun 2022 · Shift 1· Numerical answer
A capacitor of capacitance 50 pF is charged by 100 V source. It is then connected to another uncharged identical capacitor. Electrostatic energy loss in the process is ___________ nJ.
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Answer: 125
Q412022 · 27 Jun 2022 · Shift 2
1. A. $\frac{q}{ϵ _{0}}$
2. B. $\frac{q}{2 ϵ _{0}}$
3. C. $\frac{q}{4 ϵ _{0}}$
4. D. $- \frac{q}{2 π ϵ _{0}}$
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Answer: B
Q422022 · 27 Jun 2022 · Shift 2
1. A. $1 : 1$
2. B. $1 : 4$
3. C. $3 : 2$
4. D. $3 : 1$
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Answer: D
Q432022 · 27 Jun 2022 · Shift 2
1. A. $2$
2. B. $1$
3. C. $3$
4. D. $- 3$
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Answer: C
Q452022 · 27 Jun 2022 · Shift 2
Given below are two statements : Statement I : A time varying electric field is a source of changing magnetic field and vice-versa. Thus a disturbance in electric or magnetic field creates EM waves. Statement II : In a material medium, the EM wave travels with speed $v = \frac{1}{μ _{0} ϵ _{0}}$ . 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.Both Statement I and Statement II are false
3. C.Statement I is correct but Statement II is false
4. D.Statement I is incorrect but Statement II is true
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Answer: C
Q552022 · 27 Jun 2022 · Shift 2· Numerical answer
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Answer: 23
Q392022 · 26 Jun 2022 · Shift 1
1. A. $\frac{C _{1} C _{2}}{( C _{1} + C _{2} )} V$
2. B. $\frac{( C _{1} + C _{2} )}{C _{1} C _{2}} V$
3. C. $(C_{1} + C_{2}) V$
4. D. $(C_{1} - C_{2}) V$
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Answer: A
Q402022 · 26 Jun 2022 · Shift 1
Given below two statements : One is labelled as Assertion (A) and other is labelled as Reason (R). Assertion (A) : Non-polar materials do not have any permanent dipole moment. Reason (R) : When a non-polar material is placed in an electric field, the centre of the positive charge distribution of it's individual atom or molecule coincides with the centre of the negative charge distribution. In the light of above statements, choose the most appropriate answer from the options given below.
1. A.Both (A) and (R) are correct and (R) is the correct explanation of (A).
2. B.Both (A) and (R) are correct and (R) is not the correct explanation of (A).
3. C.(A) is correct but (R) is not correct.
4. D.(A) is not correct but (R) is correct.
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Answer: C
Q442022 · 26 Jun 2022 · Shift 1
If Electric field intensity of a uniform plane electromagnetic wave is given as $E = - 301.6 sin (k z - ω t) a_{x} + 452.4 sin (k z - ω t) a_{y} \frac{V}{m}$ . Then magnetic intensity 'H' of this wave in $A m^{- 1}$ will be : $[Given : Speed of light in vacuum c = 3 \times 1 0^{8} m s^{- 1}, Permeability of vacuum μ_{0} = 4 π \times 1 0^{- 7} N A^{- 2}]$
1. A. $+ 0.8 sin (k z - ω t) a_{y} + 0.8 sin (k z - ω t) a_{x}$
2. B. $+ 1.0 \times 1 0^{- 6} sin (k z - ω t) a_{y} + 1.5 \times 1 0^{- 6} (k z - ω t) a_{x}$
3. C. $- 0.8 sin (k z - ω t) a_{y} - 1.2 sin (k z - ω t) a_{x}$
4. D. $- 1.0 \times 1 0^{- 6} sin (k z - ω t) a_{y} - 1.5 \times 1 0^{- 6} sin (k z - ω t) a_{x}$
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Answer: C
Q382022 · 26 Jun 2022 · Shift 2
1. A. $60 μ C$
2. B. $130 μ C$
3. C. $260 μ C$
4. D. $585 μ C$
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Answer: A
Q392022 · 26 Jun 2022 · Shift 2
1. A. $2 μ F$
2. B. $32 μ F$
3. C. $6 μ F$
4. D. $8 μ F$
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Answer: C
Q402022 · 26 Jun 2022 · Shift 2
Sixty four conducting drops each of radius 0.02 m and each carrying a charge of $5 μ C$ are combined to form a bigger drop. The ratio of surface charge density of bigger drop to the smaller drop will be :
1. A.1 : 4
2. B.4 : 1
3. C.1 : 8
4. D.8 : 1
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Answer: B
Q382022 · 25 Jun 2022 · Shift 1
1. A. $E_{1} = σ / ε_{0}$ , $E_{2} = σ /2 ε_{0}$
2. B. $E_{1} = 2 σ / ε_{0}$ , $E_{2} = σ / ε_{0}$
3. C. $E_{1} = E_{2} = σ /2 ε_{0}$
4. D. $E_{1} = E_{2} = σ / ε_{0}$
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Answer: C
Q422022 · 25 Jun 2022 · Shift 1
The electric field in an electromagnetic wave is given by $E = 56.5 sin ω (t - x / c) NC^{- 1}$ . Find the intensity of the wave if it is propagating along x-axis in the free space. (Given : $ε_{0} = 8.85 \times 1 0^{- 12} C^{2} N^{- 1} m^{- 2}$ )
1. A. $5.65 Wm^{- 2}$
2. B. $4.24 Wm^{- 2}$
3. C. $1.9 \times 1 0^{- 7} Wm^{- 2}$
4. D. $56.5 Wm^{- 2}$
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Answer: B
Q442022 · 25 Jun 2022 · Shift 1
A light wave travelling linearly in a medium of dielectric constant $4$ , is incident on the horizontal interface separating medium with air. The angle of incidence for which the total intensity of incident wave will be reflected back into the same medium will be : (Given : relative permeability of medium $μ_{r} = 1$ )
1. A. $1 0^{\circ}$
2. B. $2 0^{\circ}$
3. C. $3 0^{\circ}$
4. D. $6 0^{\circ}$
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Answer: D
Q552022 · 25 Jun 2022 · Shift 1· Numerical answer
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Answer: 6
Q382022 · 25 Jun 2022 · Shift 2
Two metallic plates form a parallel plate capacitor. The distance between the plates is 'd'. A metal sheet of thickness $\frac{d}{2}$ and of area equal to area of each plate is introduced between the plates. What will be the ratio of the new capacitance to the original capacitance of the capacitor?
1. A. $2 : 1$
2. B. $1 : 2$
3. C. $1 : 4$
4. D. $4 : 1$
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Answer: A
Q432022 · 25 Jun 2022 · Shift 2
The electromagnetic waves travel in a medium at a speed of $2.0 \times 1 0^{8} m/s$ . The relative permeability of the medium is 1.0. The relative permittivity of the medium will be :
1. A.2.25
2. B.4.25
3. C.6.25
4. D.8.25
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Answer: A