Electrostatics & Capacitors · JEE Main previous year questions

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2022 56 questions

Q432022 · 27 Jul 2022 · Shift 2
Identify the correct statements from the following descriptions of various properties of electromagnetic waves. (A) In a plane electromagnetic wave electric field and magnetic field must be perpendicular to each other and direction of propagation of wave should be along electric field or magnetic field. (B) The energy in electromagnetic wave is divided equally between electric and magnetic fields. (C) Both electric field and magnetic field are parallel to each other and perpendicular to the direction of propagation of wave. (D) The electric field, magnetic field and direction of propagation of wave must be perpendicular to each other. (E) The ratio of amplitude of magnetic field to the amplitude of electric field is equal to speed of light. Choose the most appropriate answer from the options given below :
1. A.(D) only
2. B.(B) and (D) only
3. C.(B), (C) and (E) only
4. D.(A), (B) and (E) only
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Answer: B
Q552022 · 27 Jul 2022 · Shift 2· Numerical answer
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Answer: 10
Q562022 · 27 Jul 2022 · Shift 2· Numerical answer
A parallel plate capacitor with width $4 cm$ , length $8 cm$ and separation between the plates of $4 mm$ is connected to a battery of $20 V$ . A dielectric slab of dielectric constant 5 having length $1 cm$ , width $4 cm$ and thickness $4 mm$ is inserted between the plates of parallel plate capacitor. The electrostatic energy of this system will be ____ $ϵ_{0} J$ . (Where $ϵ_{0}$ is the permittivity of free space)
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Answer: 240
Q342022 · 26 Jul 2022 · Shift 1
The magnetic field of a plane electromagnetic wave is given by : $B = 2 \times 1 0^{- 8} sin (0.5 \times 1 0^{3} x + 1.5 \times 1 0^{11} t) \hat{j} T .$ The amplitude of the electric field would be :
1. A. $6 V m^{- 1}$ along $x$ -axis
2. B. $3 V m^{- 1}$ along $z$ -axis
3. C. $6 V m^{- 1}$ along $z$ -axis
4. D. $2 \times 1 0^{- 8} V m^{- 1}$ along $z$ -axis
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Answer: C
Q352022 · 26 Jul 2022 · Shift 1
In a series $L R$ circuit $X_{L} = R$ and power factor of the circuit is $P_{1}$ . When capacitor with capacitance $C$ such that $X_{L} = X_{C}$ is put in series, the power factor becomes $P_{2}$ . The ratio $\frac{P _{1}}{P _{2}}$ is:
1. A. $\frac{1}{2}$
2. B. $\frac{1}{2}$
3. C. $\frac{3}{2}$
4. D. $2 : 1$
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Answer: B
Q392022 · 26 Jul 2022 · Shift 1
The total charge on the system of capacitors $C_{1} = 1 μ F$ , $C_{2} = 2 μ F$ , $C_{3} = 4 μ F$ and $C_{4} = 3 μ F$ connected in parallel is : (Assume a battery of $20 V$ is connected to the combination)
1. A. $200 μ C$
2. B. $200 C$
3. C. $10 μ C$
4. D. $10 C$
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Answer: A
Q542022 · 26 Jul 2022 · Shift 1· Numerical answer
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Answer: 60
Q352022 · 25 Jul 2022 · Shift 2
Capacitance of an isolated conducting sphere of radius $R_{1}$ becomes $n$ times when it is enclosed by a concentric conducting sphere of radius $R_{2}$ connected to earth. The ratio of their radii $(\frac{R _{2}}{R _{1}})$ is :
1. A. $\frac{n}{n - 1}$
2. B. $\frac{2 n}{2 n + 1}$
3. C. $\frac{n + 1}{n}$
4. D. $\frac{2 n + 1}{n}$
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Answer: A
Q562022 · 25 Jul 2022 · Shift 2· Numerical answer
Two parallel plate capacitors of capacity C and 3C are connected in parallel combination and charged to a potential difference 18 V. The battery is then disconnected and the space between the plates of the capacitor of capacity C is completely filled with a material of dielectric constant 9. The final potential difference across the combination of capacitors will be ___________ V.
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Answer: 6
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