Electrostatics & Capacitors · JEE Main previous year questions

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2021 35 questions

Q312021 · 1 Sept 2021 · Shift 2
1. A. $3.8 \times 1 0^{- 11} C$
2. B. $8.3 \times 1 0^{- 11} C$
3. C. $3.8 \times 1 0^{- 12} C$
4. D. $8.3 \times 1 0^{- 12} C$
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Answer: B
Q462021 · 1 Sept 2021 · Shift 2
A capacitor is connected to a $20 V$ battery through a resistance of $10 Ω$ . It is found that the potential difference across the capacitor rises to $2 V$ in $1 μ s$ . The capacitance of the capacitor is ____ $μ F$ . Given : $ln (\frac{10}{9}) = 0.105$
1. A.9.52
2. B.0.95
3. C.0.105
4. D.1.85
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Answer: B
Q482021 · 1 Sept 2021 · Shift 2
Electric field of plane electromagnetic wave propagating through a non-magnetic medium is given by $E = 20 cos (2 \times 1 0^{10} t - 200 x) V/m$ . The dielectric constant of the medium is equal to : (Take $μ_{r} = 1$ )
1. A.9
2. B.2
3. C. $\frac{1}{3}$
4. D.3
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Answer: A
Q372021 · 26 Aug 2021 · Shift 2
The two thin coaxial rings, each of radius 'a' and having charges $+ Q$ and $- Q$ respectively are separated by a distance of 's'. The potential difference between the centres of the two rings is :
1. A. $\frac{Q}{2 π ε _{0}} [\frac{1}{a} + \frac{1}{s ^{2} + a ^{2}}]$
2. B. $\frac{Q}{4 π ε _{0}} [\frac{1}{a} + \frac{1}{s ^{2} + a ^{2}}]$
3. C. $\frac{Q}{4 π ε _{0}} [\frac{1}{a} - \frac{1}{s ^{2} + a ^{2}}]$
4. D. $\frac{Q}{2 π ε _{0}} [\frac{1}{a} - \frac{1}{s ^{2} + a ^{2}}]$
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Answer: D
Q402021 · 26 Aug 2021 · Shift 2
1. A. $\frac{ε _{0} A}{d} (\frac{1}{2} + \frac{K _{1} K _{2}}{K _{1} + K _{2}})$
2. B. $\frac{ε _{0} A}{d} (\frac{1}{2} + \frac{K _{1} K _{2}}{2 ( K _{1} + K _{2} )})$
3. C. $\frac{ε _{0} A}{d} (\frac{1}{2} + \frac{K _{1} + K _{2}}{K _{1} K _{2}})$
4. D. $\frac{ε _{0} A}{d} (\frac{1}{2} + \frac{2 ( K _{1} + K _{2} )}{K _{1} K _{2}})$
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Answer: A
Q452021 · 26 Aug 2021 · Shift 2
1. A. $5.9 A$
2. B. $3.16 A$
3. C. $0.94 A$
4. D. $6 A$
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Answer: B
Q362021 · 27 Jul 2021 · Shift 2
Match List I with List II. $(a) (b) (c) (d) List - I Capacitance, C Permittivity of free space, ε_{0} Permeability of free space, μ_{0} Electric field, E (i) (ii) (iii) (iv) List - II M^{1} L^{1} T^{- 3} A^{- 1} M^{- 1} L^{- 3} T^{4} A^{2} M^{- 1} L^{- 2} T^{4} A^{2} M^{1} L^{1} T^{- 2} A^{- 2}$ Choose the correct answer from the options given below
1. A.(a) $\to$ (iii), (b) $\to$ (ii), (c) $\to$ (iv), (d) $\to$ (i)
2. B.(a) $\to$ (iii), (b) $\to$ (iv), (c) $\to$ (ii), (d) $\to$ (i)
3. C.(a) $\to$ (iv), (b) $\to$ (ii), (c) $\to$ (iii), (d) $\to$ (i)
4. D.(a) $\to$ (iv), (b) $\to$ (iii), (c) $\to$ (ii), (d) $\to$ (i)
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Answer: A
Q392021 · 27 Jul 2021 · Shift 2
1. A. $tan^{- 1} [\frac{q}{m g} \times \frac{C _{1} ( V _{2} - V _{1} )}{( C _{1} + C _{2} ) ( d - t )}]$
2. B. $tan^{- 1} [\frac{q}{m g} \times \frac{C _{2} ( V _{2} - V _{1} )}{( C _{1} + C _{2} ) ( d - t )}]$
3. C. $tan^{- 1} [\frac{q}{m g} \times \frac{C _{2} ( V _{1} + V _{2} )}{( C _{1} + C _{2} ) ( d - t )}]$
4. D. $tan^{- 1} [\frac{q}{m g} \times \frac{C _{1} ( V _{1} + V _{2} )}{( C _{1} + C _{2} ) ( d - t )}]$
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Answer: C
Q432021 · 27 Jul 2021 · Shift 2
1. A. $\frac{1}{4 π ε _{0}} \frac{q}{l ^{2}}$
2. B. $\frac{1}{4 π ε _{0}} \frac{q}{( 2 l ^{2} )} (22 - 1)$
3. C. $\frac{q}{4 π ε _{0} ( 2 l ) ^{2}}$
4. D. $\frac{1}{4 π ε _{0}} \frac{2 q}{2 l ^{2}} (2)$
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Answer: B
Q372021 · 25 Jul 2021 · Shift 1
A parallel plate capacitor with plate area 'A' and distance of separation 'd' is filled with a dielectric. What is the capacity of the capacitor when permittivity of the dielectric varies as : $ε (x) = ε_{0} + k x$ , for $(0 < x \leq \frac{d}{2})$ $ε (x) = ε_{0} + k (d - x)$ , for $(\frac{d}{2} \leq x \leq d)$
1. A. $(ε_{0} + \frac{k d}{2})^{2/ k A}$
2. B. $\frac{k A}{2 l n ( \frac{2 ε _{0} + k d}{2 ε _{0}} )}$
3. C.0
4. D. $\frac{k A}{2} ln (\frac{2 ε _{0}}{2 ε _{0} - k d})$
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Answer: B
Q382021 · 25 Jul 2021 · Shift 2
If $q_{f}$ is the free charge on the capacitor plates and $q_{b}$ is the bound charge on the dielectric slab of dielectric constant k placed between the capacitor plates, then bound charge $q_{b}$ an be expressed as :
1. A. $q_{b} = q_{f} (1 - \frac{1}{k})$
2. B. $q_{b} = q_{f} (1 - \frac{1}{k})$
3. C. $q_{b} = q_{f} (1 + \frac{1}{k})$
4. D. $q_{b} = q_{f} (1 + \frac{1}{k})$
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Answer: B
Q402021 · 25 Jul 2021 · Shift 2
1. A. $\frac{3}{8}$
2. B. $\frac{3}{2}$
3. C. $\frac{2}{3}$
4. D. $\frac{4}{3}$
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Answer: C
Q382021 · 22 Jul 2021 · Shift 2
An electric dipole is placed on x-axis in proximity to a line charge of linear charge density $3.0 \times 1 0^{- 6} C/m$ . Line charge is placed on z-axis and positive and negative charge of dipole is at a distance of $10 mm$ and $12 mm$ from the origin respectively. If total force of $4 N$ is exerted on the dipole, find out the amount of positive or negative charge of the dipole.
1. A. $0.485 mC$
2. B. $815.1 nC$
3. C. $8.8 μ C$
4. D. $4.44 μ C$
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Answer: D
Q552021 · 22 Jul 2021 · Shift 2· Numerical answer
The total charge enclosed in an incremental volume of $2 \times 1 0^{- 9} m^{3}$ located at the origin is ________ nC, if electric flux density of its field is found as $D = e^{- x} sin y \hat{i} - e^{- x} cos y \hat{j} + 2 z \hat{k} C/m^{2}$
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Answer: 4
Q332021 · 20 Jul 2021 · Shift 1
A current of $5 A$ is passing through a non-linear magnesium wire of cross-section $0.04 m^{2}$ . At every point the direction of current density is at an angle of $6 0^{\circ}$ with the unit vector of area of cross-section. The magnitude of electric field at every point of the conductor is : (Resistivity of magnesium $ρ = 44 \times 1 0^{- 8} Ω m$ )
1. A. $11 \times 1 0^{- 5} V/m$
2. B. $11 \times 1 0^{- 3} V/m$
3. C. $11 \times 1 0^{- 7} V/m$
4. D. $11 \times 1 0^{- 2} V/m$
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Answer: A
Q382021 · 20 Jul 2021 · Shift 1
A certain charge Q is divided into two parts q and $(Q - q)$ . How should the charges Q and q be divided so that q and $(Q - q)$ placed at a certain distance apart experience maximum electrostatic repulsion?
1. A. $Q = 2 q$
2. B. $Q = 4 q$
3. C. $Q = 3 q$
4. D. $Q = \frac{q}{2}$
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Answer: A
Q462021 · 20 Jul 2021 · Shift 1
AC voltage $V (t) = 20 sin ω t$ of frequency $50 Hz$ is applied to a parallel plate capacitor. The separation between the plates is $2 mm$ and the area is $1 m^{2}$ . The amplitude of the oscillating displacement current for the applied AC voltage is ________. [Take $ε_{0} = 8.85 \times 1 0^{- 12} F/m$ ]
1. A. $55.58 μ A$
2. B. $21.14 μ A$
3. C. $27.79 μ A$
4. D. $83.37 μ A$
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Answer: C
Q512021 · 20 Jul 2021 · Shift 1· Numerical answer
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Answer: 1
Q312021 · 18 Mar 2021 · Shift 1
An oil drop of radius $2 mm$ with a density $3 g cm^{- 3}$ is held stationary under a constant electric field $3.55 \times 1 0^{5} V m^{- 1}$ in the Millikan's oil drop experiment. What is the number of excess electrons that the oil drop will possess? (consider $g = 9.81 m/s^{2}$ )
1. A. $48.8 \times 1 0^{11}$
2. B. $1.73 \times 1 0^{10}$
3. C. $17.3 \times 1 0^{10}$
4. D. $1.73 \times 1 0^{12}$
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Answer: B
Q322021 · 18 Mar 2021 · Shift 1
Imagine that the electron in a hydrogen atom is replaced by a muon $(μ)$ . The mass of muon particle is 207 times that of an electron and charge is equal to the charge of an electron. The ionization potential of this hydrogen atom will be :
1. A. $13.6 eV$
2. B. $2815.2 eV$
3. C. $331.2 eV$
4. D. $27.2 eV$
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Answer: B
Q522021 · 18 Mar 2021 · Shift 1· Numerical answer
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Answer: 2
Q562021 · 18 Mar 2021 · Shift 1· Numerical answer
A parallel plate capacitor has plate area $100 m^{2}$ and plate separation of 10 m. The space between the plates is filled up to a thickness 5 m with a material of dielectric constant of 10. The resultant capacitance of the system is 'x' pF. The value of $ε_{0} = 8.85 \times 1 0^{- 12} F.m^{- 1}$ . The value of 'x' to the nearest integer is _______.
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Answer: 161
Q312021 · 18 Mar 2021 · Shift 2
A plane electromagnetic wave propagating along y-direction can have the following pair of electric field $(E)$ and magnetic field $(B)$ components.
1. A. $E_{x}, B_{z}$ or $E_{z}, B_{x}$
2. B. $E_{x}, B_{y}$ or $E_{y}, B_{x}$
3. C. $E_{y}, B_{y}$ or $E_{z}, B_{z}$
4. D. $E_{y}, B_{x}$ or $E_{x}, B_{y}$
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Answer: A
Q392021 · 16 Mar 2021 · Shift 1
For changing the capacitance of a given parallel plate capacitor, a dielectric material of dielectric constant K is used, which has the same area as the plates of the capacitor. The thickness of the dielectric slab is $\frac{3}{4} d$ , where 'd' is the separation between the plates of parallel plate capacitor. The new capacitance ( $C^{'}$ ) in terms of original capacitance ( $C_{0}$ ) is given by the following relation :
1. A. $C^{'} = \frac{3 + K}{4 K} C_{0}$
2. B. $C^{'} = \frac{4 + K}{3} C_{0}$
3. C. $C^{'} = \frac{4 K}{K + 3} C_{0}$
4. D. $C^{'} = \frac{4}{3 + K} C_{0}$
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Answer: C
Q402021 · 16 Mar 2021 · Shift 1
A plane electromagnetic wave of frequency 500 MHz is travelling in vacuum along y-direction. At a particular point in space and time, $B = 8.0 \times 1 0^{- 8} \overset{z}{^} T$ . The value of electric field at this point is : (speed of light = $3 \times 1 0^{8} m s^{- 1}$ ) $\overset{x}{^}, \overset{y}{^}, \overset{z}{^}$ are unit vectors along x, y and z directions.
1. A. $2.6 \overset{x}{^} V/m$
2. B. $- 24 \overset{x}{^} V/m$
3. C. $24 \overset{x}{^} V/m$
4. D. $- 2.6 \overset{y}{^} V/m$
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Answer: B