Electrostatics & Capacitors · JEE Main previous year questions

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2022 56 questions

Q402022 · 29 Jul 2022 · Shift 1
1. A. $\frac{ρ _{0} r}{4 ε _{0}} (\frac{3}{4} - \frac{r}{R})$
2. B. $\frac{ρ _{0} r}{3 ε _{0}} (\frac{3}{4} - \frac{r}{R})$
3. C. $\frac{ρ _{0} r}{4 ε _{0}} (1 - \frac{r}{R})$
4. D. $\frac{ρ _{0} r}{5 ε _{0}} (1 - \frac{r}{R})$
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Answer: C
Q412022 · 29 Jul 2022 · Shift 1
Given below are two statements. Statement I : Electric potential is constant within and at the surface of each conductor. Statement II : Electric field just outside a charged conductor is perpendicular to the surface of the conductor at every point. In the light of the above statements, choose the most appropriate answer from the options given below.
1. A.Both Statement I and Statement II are correct
2. B.Both Statement I and Statement II are incorrect
3. C.Statement I is correct but Statement II is incorrect
4. D.Statement I is incorrect but Statement II is correct
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Answer: A
Q602022 · 29 Jul 2022 · Shift 1· Numerical answer
If the potential barrier across a p-n junction is $0.6 V$ . Then the electric field intensity, in the depletion region having the width of $6 \times 1 0^{- 6} m$ , will be ____ $\times 1 0^{5} N/C$ .
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Answer: 1
Q312022 · 29 Jul 2022 · Shift 2
Two identical metallic spheres A and B when placed at certain distance in air repel each other with a force of $F$ . Another identical uncharged sphere C is first placed in contact with A and then in contact with B and finally placed at midpoint between spheres A and B. The force experienced by sphere C will be:
1. A. $3 F /2$
2. B. $3 F /4$
3. C. $F$
4. D. $2 F$
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Answer: B
Q332022 · 29 Jul 2022 · Shift 2
Two identical thin metal plates have charges $q_{1}$ and $q_{2}$ respectively such that $q_{1} > q_{2}$ . The plates were brought close to each other to form a parallel plate capacitor of capacitance C. The potential difference between them is :
1. A. $\frac{( q _{1} + q _{2} )}{C}$
2. B. $\frac{( q _{1} - q _{2} )}{C}$
3. C. $\frac{( q _{1} - q _{2} )}{2 C}$
4. D. $\frac{2 ( q _{1} - q _{2} )}{C}$
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Answer: C
Q582022 · 29 Jul 2022 · Shift 2· Numerical answer
A capacitor of capacitance $500 μ F$ is charged completely using a dc supply of $100 V$ . It is now connected to an inductor of inductance $50 mH$ to form an LC circuit. The maximum current in LC circuit will be ____ $A$ .
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Answer: 10
Q392022 · 28 Jul 2022 · Shift 1
Two capacitors, each having capacitance $40 μ F$ are connected in series. The space between one of the capacitors is filled with dielectric material of dielectric constant $K$ such that the equivalence capacitance of the system became $24 μ F$ . The value of $K$ will be :
1. A.1.5
2. B.2.5
3. C.1.2
4. D.3
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Answer: A
Q542022 · 28 Jul 2022 · Shift 1· Numerical answer
Two electric dipoles of dipole moments $1.2 \times 1 0^{- 30} Cm$ and $2.4 \times 1 0^{- 30} Cm$ are placed in two different uniform electric fields of strengths $5 \times 1 0^{4} NC^{- 1}$ and $15 \times 1 0^{4} NC^{- 1}$ respectively. The ratio of maximum torque experienced by the electric dipoles will be $\frac{1}{x}$ . The value of $x$ is _________.
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Answer: 6
Q392022 · 28 Jul 2022 · Shift 2
A slab of dielectric constant $K$ has the same cross-sectional area as the plates of a parallel plate capacitor and thickness $\frac{3}{4} d$ , where $d$ is the separation of the plates. The capacitance of the capacitor when the slab is inserted between the plates will be : (Given $C_{0} = capacitance of capacitor with air as medium between plates$ .)
1. A. $\frac{4 K C _{0}}{3 + K}$
2. B. $\frac{3 K C _{0}}{3 + K}$
3. C. $\frac{3 + K}{4 K C _{0}}$
4. D. $\frac{K}{4 + K}$
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Answer: A
Q402022 · 28 Jul 2022 · Shift 2
1. A. $tan^{- 1} (4)$
2. B. $tan^{- 1} (2)$
3. C. $tan^{- 1} (\frac{1}{3})$
4. D. $tan^{- 1} (3)$
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Answer: B
Q432022 · 27 Jul 2022 · Shift 1
A beam of light travelling along $X$ -axis is described by the electric field $E_{y} = 900 sin ω (t - x / c)$ . The ratio of electric force to magnetic force on a charge $q$ moving along $Y$ -axis with a speed of $3 \times 1 0^{7} ms^{- 1}$ will be : (Given speed of light $= 3 \times 1 0^{8} ms^{- 1}$ )
1. A. $1 : 1$
2. B. $1 : 10$
3. C. $10 : 1$
4. D. $1 : 2$
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Answer: C
Q452022 · 27 Jul 2022 · Shift 1
An electron (mass $m$ ) with an initial velocity $v = v_{0} \hat{i} (v_{0} > 0)$ is moving in an electric field $E = - E_{0} \hat{i} (E_{0} > 0)$ where $E_{0}$ is constant. If at $t = 0$ de Broglie wavelength is $λ_{0} = \frac{h}{m v _{0}}$ , then its de Broglie wavelength after time t is given by
1. A. $λ_{0}$
2. B. $λ_{0} (1 + \frac{e E _{0} t}{m v _{0}})$
3. C. $λ_{0} t$
4. D. $\frac{λ _{0}}{( 1 + \frac{e E _{0} t}{m v _{0}} )}$
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Answer: D
Q542022 · 27 Jul 2022 · Shift 1· Numerical answer
To light, a $50 W, 100 V$ lamp is connected, in series with a capacitor of capacitance $\frac{50}{π x} μ F$ , with $200 V, 50 Hz$ AC source. The value of $x$ will be _________.
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Answer: 3
Q552022 · 27 Jul 2022 · Shift 1· Numerical answer
A $1 m$ long copper wire carries a current of $1 A$ . If the cross section of the wire is $2.0 mm^{2}$ and the resistivity of copper is $1.7 \times 1 0^{- 8} Ω m$ , the force experienced by moving electron in the wire is _________ $\times 1 0^{- 23} N$ . (charge on electron $= 1.6 \times 1 0^{- 19} C$ )
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Answer: 136
Q562022 · 27 Jul 2022 · Shift 1· Numerical answer
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Answer: 1
Q392022 · 27 Jul 2022 · Shift 2
A charge of $4 μ C$ is to be divided into two. The distance between the two divided charges is constant. The magnitude of the divided charges so that the force between them is maximum, will be :
1. A. $1 μ C$ and $3 μ C$
2. B. $2 μ C$ and $2 μ C$
3. C. $0$ and $4 μ C$
4. D. $1.5 μ C$ and $2.5 μ C$
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Answer: B
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