JEE Physics Magnetism and Matter MCQs Set 36

Practice MCQs for JEE Physics Magnetism and Matter

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Multiple Choice Questions

Question 1: A magnetic compass needle oscillates 30 times per minute at a place where the dip is \( 45^\circ \) and 40 times per minute where the dip is \( 30^\circ \). If \( B_1 \) and \( B_2 \) are the total magnetic fields of the Earth at the two places, the ratio \( B_1/B_2 \) is best given by
(a) 0.7
(b) 1.8
(c) 3.6
(d) 2.2
Show Answer & Explanation

Answer: (a) 0.7

Explanation:
1. The needle swings in the horizontal plane, so \( f^2\propto B_H=B\cos\delta \).
2. \( \dfrac{B_1}{B_2}=\dfrac{30^2/\cos45^\circ}{40^2/\cos30^\circ}=\dfrac{900\times1.414}{1600\times1.155}=0.69\approx0.7 \).

Teacher's Note:
1. Identify whether the situation involves a dipole in a field, the Earth's field or a material property, and write the relevant relation.
2. Check the units and the order of magnitude of the result.

Question 2: A moving coil galvanometer has a coil with 175 turns and area 1 cm\(^2\), with a torsion band of torsion constant \( 10^{-6} \) N m/rad. The coil is in a magnetic field B parallel to its plane (radial field). The coil deflects by \( 1^\circ \) for a current of 1 mA. B is approximately
(a) \( 10^{-4} \) T
(b) \( 10^{-3} \) T
(c) \( 10^{-1} \) T
(d) \( 10^{-2} \) T
Show Answer & Explanation

Answer: (b) \( 10^{-3} \) T

Explanation:
1. Balance: \( NIAB=C\theta \Rightarrow B=\dfrac{C\theta}{NIA} \).
2. \( B=\dfrac{10^{-6}\times(\pi/180)}{175\times10^{-3}\times10^{-4}}=1.0\times10^{-3} \) T.

Teacher's Note:
1. Identify whether the situation involves a dipole in a field, the Earth's field or a material property, and write the relevant relation.
2. Check the units and the order of magnitude of the result.

Question 3: A paramagnetic material has \( 10^{28} \) atoms per m\(^3\). Its magnetic susceptibility at 350 K is \( 2.8\times10^{-4} \). Its susceptibility at 300 K is
(a) \( 3.726\times10^{-4} \)
(b) \( 3.672\times10^{-4} \)
(c) \( 3.267\times10^{-4} \)
(d) \( 2.672\times10^{-4} \)
Show Answer & Explanation

Answer: (c) \( 3.267\times10^{-4} \)

Explanation:
1. Curie's law: \( \chi\propto\dfrac1T \).
2. \( \chi_{300}=2.8\times10^{-4}\times\dfrac{350}{300}=3.267\times10^{-4} \).

Teacher's Note:
1. Identify whether the situation involves a dipole in a field, the Earth's field or a material property, and write the relevant relation.
2. Check the units and the order of magnitude of the result.

Question 4: A paramagnetic substance in the form of a cube with sides 1 cm has a magnetic dipole moment of \( 20\times10^{-6} \) J/T when a magnetic intensity of \( 60\times10^3 \) A/m is applied. Its magnetic susceptibility is
(a) \( 3.3\times10^{-2} \)
(b) \( 4.3\times10^{-2} \)
(c) \( 2.3\times10^{-2} \)
(d) \( 3.3\times10^{-4} \)
Show Answer & Explanation

Answer: (d) \( 3.3\times10^{-4} \)

Explanation:
1. Magnetisation \( M=\dfrac{m}{V}=\dfrac{20\times10^{-6}}{10^{-6}}=20 \) A/m.
2. \( \chi=\dfrac MH=\dfrac{20}{60\times10^3}=3.3\times10^{-4} \).

Teacher's Note:
1. Identify whether the situation involves a dipole in a field, the Earth's field or a material property, and write the relevant relation.
2. Check the units and the order of magnitude of the result.

Question 5: At some location the horizontal component of the Earth's magnetic field is \( 18\times10^{-6} \) T. A magnetic needle of length 0.12 m and pole strength 1.8 A m is suspended from its mid-point by a thread and makes \( 45^\circ \) with the horizontal in equilibrium. To keep the needle horizontal, the vertical force that should be applied at one of its ends is
(a) \( 6.5\times10^{-5} \) N
(b) \( 3.6\times10^{-5} \) N
(c) \( 1.3\times10^{-5} \) N
(d) \( 1.8\times10^{-5} \) N
Show Answer & Explanation

Answer: (a) \( 6.5\times10^{-5} \) N

Explanation:
1. Magnetic moment \( M=m\cdot l=1.8\times0.12=0.216 \) A m\(^2\); total field \( B=\dfrac{18\times10^{-6}}{\cos45^\circ}=25.5\times10^{-6} \) T.
2. Torque to hold it \( 45^\circ \) off the field: \( \tau=MB\sin45^\circ=3.89\times10^{-6} \) N m. A force F at one end acts at arm 0.06 m: \( F=\dfrac{3.89\times10^{-6}}{0.06}=6.5\times10^{-5} \) N.

Teacher's Note:
1. Identify whether the situation involves a dipole in a field, the Earth's field or a material property, and write the relevant relation.
2. Check the units and the order of magnitude of the result.

Question 6: A bar magnet is demagnetised by inserting it inside a solenoid of length 0.2 m with 100 turns carrying a current of 5.2 A. The coercivity of the bar magnet is close to
(a) 1200 A/m
(b) 2600 A/m
(c) 285 A/m
(d) 520 A/m
Show Answer & Explanation

Answer: (b) 2600 A/m

Explanation:
1. \( H=nI=\dfrac{N}{L}I \).
2. \( H=\dfrac{100}{0.2}\times5.2=2600 \) A/m.

Teacher's Note:
1. Identify whether the situation involves a dipole in a field, the Earth's field or a material property, and write the relevant relation.
2. Check the units and the order of magnitude of the result.

Question 7: Statement I: the sensitivity of a moving coil galvanometer is increased by placing a suitable magnetic material as a core inside the coil. Statement II: soft iron has a high magnetic permeability and cannot be easily magnetised or demagnetised. Which is correct?
(a) Both are true and II explains I
(b) Both are true but II does not explain I
(c) Statement I is true; Statement II is false
(d) Statement I is false; Statement II is true
Show Answer & Explanation

Answer: (c) Statement I is true; Statement II is false

Explanation:
1. A soft iron core concentrates the field, so the torque per unit current increases and Statement I is true.
2. Soft iron has high permeability but low retentivity and coercivity, so it is easily magnetised and demagnetised; Statement II is false.

Teacher's Note:
1. Identify whether the situation involves a dipole in a field, the Earth's field or a material property, and write the relevant relation.
2. Check the units and the order of magnitude of the result.

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