Magnetic Effects of Current & Magnetism · JEE Main previous year questions

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2020 22 questions

Q432020 · 6 Sept 2020 · Shift 1
A particle of charge q and mass m is moving with a velocity $- v \hat{i}$ ( $v \neq = 0$ ) towards a large screen placed in the Y - Z plane at a distance d. If there is a magnetic field $B = B_{0} \hat{k}$ , the maximum value of v for which the particle will not hit the screen is :
1. A. $\frac{2 q d B _{0}}{m}$
2. B. $\frac{q d B _{0}}{3 m}$
3. C. $\frac{q d B _{0}}{2 m}$
4. D. $\frac{q d B _{0}}{m}$
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Answer: D
Q292020 · 6 Sept 2020 · Shift 2
A charged particle going around in a circle can be considered to be a current loop. A particle of mass m carrying charge q is moving in a plane with speed v under the influence of magnetic field $B$ . The magnetic moment of this moving particle:
1. A. $\frac{m v ^{2} B}{2 B ^{2}}$
2. B. $- \frac{m v ^{2} B}{2 B ^{2}}$
3. C. $- \frac{m v ^{2} B}{B ^{2}}$
4. D. $- \frac{m v ^{2} B}{2 π B ^{2}}$
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Answer: B
Q312020 · 3 Sept 2020 · Shift 1
A charged particle carrying charge $1 μ C$ is moving with velocity $(2 \hat{i} + 3 \hat{j} + 4 \hat{k}) m s^{- 1}$ . If an external magnetic field of $(5 \hat{i} + 3 \hat{j} - 6 \hat{k}) \times 1 0^{- 3} T$ exists in the region where the particle is moving then the force on the particle is $F \times 1 0^{- 9} N$ . The vector $F$ is :
1. A. $- 0.30 \hat{i} + 0.32 \hat{j} - 0.09 \hat{k}$
2. B. $- 300 \hat{i} + 320 \hat{j} - 90 \hat{k}$
3. C. $- 30 \hat{i} + 32 \hat{j} - 9 \hat{k}$
4. D. $- 3.0 \hat{i} + 3.2 \hat{j} - 0.9 \hat{k}$
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Answer: C
Q422020 · 3 Sept 2020 · Shift 1
Magnitude of magnetic field (in SI units) at the centre of a hexagonal shape coil of side 10 cm, 50 turns and carrying current I (Ampere) in units of $\frac{μ _{0} I}{π}$ is :
1. A. $2503$
2. B. $53$
3. C. $5003$
4. D. $503$
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Answer: C
Q372020 · 3 Sept 2020 · Shift 2
1. A. $B$
2. B.zero
3. C.much large than $∣ B ∣$ and parallel to $B$
4. D.much large than $∣ B ∣$ but opposite to $B$
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Answer: B
Q402020 · 3 Sept 2020 · Shift 2
A uniform magnetic field B exists in a direction perpendicular to the plane of a square loop made of a metal wire. The wire has a diameter of 4 mm and a total length of 30 cm. The magnetic field changes with time at a steady rate $\frac{d B}{d t} = 0.032 T s^{- 1}$ . The induced current in the loop is close to (Resistivity of the metal wire is $1.23 \times 1 0^{- 8} Ω m$ )
1. A.0.53 A
2. B.0.43 A
3. C.0.34 A
4. D.0.61 A
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Answer: D
Q272020 · 2 Sept 2020 · Shift 1
A plane electromagnetic wave, has frequency of $2.0 \times 1 0^{10} Hz$ and its energy density is $1.02 \times 1 0^{- 8} J/m^{3}$ in vacuum. The amplitude of the magnetic field of the wave is close to ( $\frac{1}{4 π ε _{0}} = 9 \times 1 0^{9} \frac{N m ^{2}}{C ^{2}}$ and speed of light $= 3 \times 1 0^{8} ms^{- 1}$ )
1. A.190 nT
2. B.150 nT
3. C.160 nT
4. D.180 nT
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Answer: C
Q432020 · 2 Sept 2020 · Shift 1
A beam of protons with speed $4 \times 1 0^{5} ms^{- 1}$ enters a uniform magnetic field of 0.3 T at an angle of $6 0^{\circ}$ to the magnetic field. The pitch of the resulting helical path of protons is close to : (Mass of the proton $= 1.67 \times 1 0^{- 27} kg$ , charge of the proton $= 1.69 \times 1 0^{- 19} C$ )
1. A.2 cm
2. B.12 cm
3. C.5 cm
4. D.4 cm
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Answer: D
Q502020 · 2 Sept 2020 · Shift 1· Numerical answer
A circular coil of radius $10 cm$ is placed in a uniform magnetic field of $3.0 \times 1 0^{- 5} T$ with its plane perpendicular to the field initially. It is rotated at constant angular speed about an axis along the diameter of coil and perpendicular to magnetic field so that it undergoes half of rotation in $0.2 s$ . The maximum value of EMF induced (in $μ V$ ) in the coil will be close to the integer ____.
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Answer: 15
Q332020 · 2 Sept 2020 · Shift 2
1. A.0.22 m
2. B.0.11 m
3. C.0.88 m
4. D.0.44 m
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Answer: D
Q352020 · 2 Sept 2020 · Shift 2
1. A. $2 abI$ , along $(\frac{j ^}{5} + \frac{2 k ^}{5})$
2. B. $abI$ , along $(\frac{j ^}{5} + \frac{2 k ^}{5})$
3. C. $2 abI$ , along $(\frac{j ^}{2} + \frac{k ^}{2})$
4. D. $abI$ , along $(\frac{j ^}{2} + \frac{k ^}{2})$
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Answer: C
Q312020 · 9 Jan 2020 · Shift 1
A long, straight wire of radius a carries a current distributed uniformly over its cross-section. The ratio of the magnetic fields due to the wire at distance $\frac{a}{3}$ and $2 a$ , respectively from the axis of the wire is :
1. A.2
2. B. $\frac{1}{2}$
3. C. $\frac{3}{2}$
4. D. $\frac{2}{3}$
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Answer: D
Q362020 · 9 Jan 2020 · Shift 1
Radiation, with wavelength $6561 \overset{˚}{A}$ falls on a metal surface to produce photoelectrons. The electrons are made to enter a uniform magnetic field of $3 \times 1 0^{- 4} T$ . If the radius of the largest circular path followed by the electrons is $10 mm$ , the work function of the metal is close to :
1. A.1.8eV
2. B.0.8eV
3. C.1.1eV
4. D.1.6eV
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Answer: C
Q292020 · 9 Jan 2020 · Shift 2
1. A. $\frac{e μ _{0} n I R}{4 m}$
2. B. $\frac{e μ _{0} n I R}{m}$
3. C. $\frac{e μ _{0} n I R}{2 m}$
4. D. $\frac{2 e μ _{0} n I R}{m}$
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Answer: C
Q302020 · 9 Jan 2020 · Shift 2
A plane electromagnetic wave is propagating along the direction $\frac{i ^ + j ^}{2}$ , with its polarization along the direction $\hat{k}$ . The correct form of the magnetic field of the wave would be (here $B_{0}$ is an appropriate constant) :
1. A. $B_{0} \frac{i ^ - j ^}{2} cos (ω t - k \frac{i ^ + j ^}{2})$
2. B. $B_{0} \frac{i ^ + j ^}{2} cos (ω t - k \frac{i ^ + j ^}{2})$
3. C. $B_{0} \frac{j ^ - i ^}{2} cos (ω t + k \frac{i ^ + j ^}{2})$
4. D. $B_{0} \hat{k} cos (ω t - k \frac{i ^ + j ^}{2})$
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Answer: A
Q282020 · 8 Jan 2020 · Shift 1
Proton with kinetic energy of 1MeV moves from south to north. It gets an acceleration of $1 0^{12} m/s^{2}$ by an applied magnetic field (west to east). The value of magnetic field : (Rest mass of proton is $1.6 \times 1 0^{- 27} kg$ ) :
1. A.0.71mT
2. B.7.1mT
3. C.0.071mT
4. D.71mT
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Answer: A
Q432020 · 8 Jan 2020 · Shift 1
1. A. $48 μ V$
2. B. $28 μ V$
3. C. $56 μ V$
4. D. $36 μ V$
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Answer: C
Q362020 · 8 Jan 2020 · Shift 2
1. A. $\frac{μ _{0} I}{2 π R} (π + 1)$
2. B. $\frac{μ _{0} I}{2 π R} (π - \frac{1}{2})$
3. C. $\frac{μ _{0} I}{2 R}$
4. D. $\frac{μ _{0} I}{2 π R} (π + \frac{1}{2})$
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Answer: D
Q292020 · 7 Jan 2020 · Shift 1
A long solenoid of radius R carries a time (t) - dependent current $I (t) = I_{0} t (1 - t)$ . A ring of radius 2R is placed coaxially near its middle. During the time interval $0 \leq t \leq 1$ , the induced current ( $I_{R}$ ) and the induced EMF( $V_{R}$ ) in the ring change as :
1. A.Direction of $I_{R}$ remains unchanged and $V_{R}$ is zero at t = 0.25
2. B.Direction of $I_{R}$ remains unchanged and $V_{R}$ is maximum at t = 0.5
3. C.At t = 0.25 direction of $I_{R}$ reverses and $V_{R}$ is maximum
4. D.At t = 0.5 direction of $I_{R}$ reverses and $V_{R}$ is zero
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Answer: D
Q492020 · 7 Jan 2020 · Shift 1· Numerical answer
A loop ABCDEFA of straight edges has six corner points $A (0, 0, 0)$ , $B (5, 0, 0)$ , $C (5, 5, 0)$ , $D (0, 5, 0)$ , $E (0, 5, 5)$ and $F (0, 0, 5)$ . The magnetic field in this region is $B = (3 \hat{i} + 4 \hat{k}) T$ . The quantity of flux through the loop ABCDEFA (in Wb) is ____.
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Answer: 175
Q312020 · 7 Jan 2020 · Shift 2
A planar loop of wire rotates in a uniform magnetic field. Initially at t = 0, the plane of the loop is perpendicular to the magnetic field. If it rotates with a period of 10 s about an axis in its plane then the magnitude of induced emf will be maximum and minimum, respectively at :
1. A.2.5 s and 7.5 s
2. B.5.0 s and 10.0 s
3. C.5.0 s and 7.5 s
4. D.2.5 s and 5.0 s
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Answer: D
Q432020 · 7 Jan 2020 · Shift 2
1. A.1.0 T, 50A/m and 1.5 T
2. B.1.5 T, 50 A/m and 1.0 T
3. C.1.5 T, 50 A/m and 2.0 T
4. D.150 A/m, 1.0 T and 1.5 T
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Answer: A