JEE Physics Magnetism and Matter MCQs Set 06

Answer: (c) (a) is true but (b) is false

Explanation:
1. Magnetisation is proportional to \( \frac BT \) (Curie's law) in the unsaturated region.
2. A stronger field aligns more dipoles, so (a) is true.
3. Higher temperature increases thermal randomisation, reducing magnetisation, so (b) is false.

Teacher's Note:
1. Think of competition between alignment by the field and thermal randomising.
2. Saturation occurs only at very high B and very low T.

Answer: (d) \( \mu_0=\mu(1+\chi_m) \)

Explanation:
1. The standard relations are \( B=\mu_0(H+I) \), \( B=\mu_0H(1+\chi_m) \) and \( \mu_r=1+\chi_m \).
2. Since \( \mu=\mu_0\mu_r=\mu_0(1+\chi_m) \), the correct statement is \( \mu=\mu_0(1+\chi_m) \).
3. So \( \mu_0=\mu(1+\chi_m) \) is wrong.

Teacher's Note:
1. Memorise: \( \mu=\mu_0(1+\chi_m) \).
2. The other three are consistent with it.

Answer: (a) tall and wide

Explanation:
1. A permanent magnet needs large retentivity (tall loop) so it keeps a strong magnetisation.
2. It needs large coercivity (wide loop) so that it is not easily demagnetised.
3. So the loop is tall and wide.

Teacher's Note:
1. Soft iron has the opposite requirement: small area loop.
2. Loop area represents energy lost per cycle.

Answer: (b) high retentivity and high coercivity

Explanation:
1. High retentivity gives a strong residual magnetisation.
2. High coercivity makes the magnetisation hard to remove.
3. Steel and alnico are suitable.

Teacher's Note:
1. Soft iron is the opposite case.
2. Both properties are needed together.

Answer: (c) (a) and (b) are true

Explanation:
1. Soft iron is almost pure iron, a metal, so it conducts electricity: (a) is true, and it is a magnetic material (ferromagnetic): (b) is true.
2. It is nearly pure iron, not an alloy: (c) is false.
3. Its coercivity is low, so it is unsuitable for permanent magnets: (d) is false.

Teacher's Note:
1. Soft iron is used in electromagnets and transformer cores.
2. Permanent magnets use steel or alloys.

Answer: (d) low hysteresis loss and high permeability

Explanation:
1. Soft iron has a narrow hysteresis loop, so energy loss per cycle is small.
2. It has high permeability, so it gives a strong field for a given current.
3. These are the properties needed for transformer cores and electromagnets.

Teacher's Note:
1. Loop area gives hysteresis loss.
2. Reversing the magnetisation thousands of times per second makes low loss essential.

Answer: (a) 0.01 N m

Explanation:
1. Torque: \( \tau=\mu B\sin\theta \).
2. Substitute: \( 0.5\times0.04\times\sin30^\circ=0.5\times0.04\times0.5 \).
3. This gives \( \tau=0.01 \) N m.

Teacher's Note:
1. Maximum torque occurs at 90 degrees.
2. The torque tries to align the needle with the field.