Magnetism and Matter Chapter-Wise Test 4

Correct answer Carries: 4.

Wrong Answer Carries: -1.

A material with \( \mu_r = 250 \) and \( H = 700 \, \text{A m}^{-1} \) has \( B \): (Take \( \mu_0 = 4\pi \times 10^{-7} \, \text{T m A}^{-1} \)).

\( B = \mu_0 \mu_r H \).

Given: \( \mu_r = 250 \), \( H = 700 \, \text{A m}^{-1} \), \( \mu_0 = 4\pi \times 10^{-7} \).

\( B = 4\pi \times 10^{-7} \times 250 \times 700 = 0.2198 \, \text{T} \approx 0.22 \, \text{T} \).

0.20 T
0.21 T
0.22 T
0.23 T
3

The magnetic field contribution \( B_m \) due to a material with \( M = 2.5 \times 10^5 \, \text{A m}^{-1} \) is: (Take \( \mu_0 = 4\pi \times 10^{-7} \, \text{T m A}^{-1} \)).

\( B_m = \mu_0 M \).

Given: \( M = 2.5 \times 10^5 \, \text{A m}^{-1} \), \( \mu_0 = 4\pi \times 10^{-7} \).

\( B_m = 4\pi \times 10^{-7} \times 2.5 \times 10^5 = 0.314 \, \text{T} \approx 0.31 \, \text{T} \).

0.28 T
0.30 T
0.31 T
0.33 T
3

A magnetic dipole experiences a torque of \( 0.02 \, \text{N m} \) in a field of \( 0.4 \, \text{T} \) at \( 90^\circ \). What is its magnetic moment?

\( \tau = m B \sin\theta \), so \( m = \frac{\tau}{B \sin\theta} \).

Given: \( \tau = 0.02 \, \text{N m} \), \( B = 0.4 \, \text{T} \), \( \theta = 90^\circ \), \( \sin 90^\circ = 1 \).

\( m = \frac{0.02}{0.4 \times 1} = 0.05 \, \text{A m}^2 \).

0.02 A m²
0.05 A m²
0.08 A m²
0.1 A m²
2

The magnetic field lines of a solenoid resemble those of a bar magnet because:

A solenoid’s field lines emerge from one end (acting as a north pole) and enter the other (acting as a south pole), mirroring a bar magnet’s dipole field pattern due to the cumulative effect of current loops behaving like a magnetic dipole.

The field is uniform throughout
The field lines are straight
It acts as a magnetic dipole
It contains no poles
3

The magnetic field lines of a bar magnet are closest together:

Magnetic field lines are closest together near the poles of a bar magnet, where the field strength is greatest, as the density of lines reflects the magnitude of the magnetic field.

At the center of the magnet
Near the poles
Midway along its length
Far from the magnet
2

A solenoid with 800 turns per meter and current \( 1.5 \, \text{A} \) has a core with \( \mu_r = 300 \). What is \( B \) inside? (Take \( \mu_0 = 4\pi \times 10^{-7} \, \text{T m A}^{-1} \)).

\( B = \mu_0 \mu_r n I \).

Given: \( n = 800 \, \text{m}^{-1} \), \( I = 1.5 \, \text{A} \), \( \mu_r = 300 \), \( \mu_0 = 4\pi \times 10^{-7} \).

\( B = 4\pi \times 10^{-7} \times 300 \times 800 \times 1.5 = 0.452 \, \text{T} \approx 0.45 \, \text{T} \).

0.40 T
0.45 T
0.50 T
0.55 T
2

A magnetic dipole of moment \( 0.3 \, \text{A m}^2 \) is in a uniform field of \( 0.7 \, \text{T} \) at \( 30^\circ \). What is the torque on it?

Torque is \( \tau = m B \sin\theta \).

Given: \( m = 0.3 \, \text{A m}^2 \), \( B = 0.7 \, \text{T} \), \( \theta = 30^\circ \), \( \sin 30^\circ = 0.5 \).

Substitute: \( \tau = 0.3 \times 0.7 \times 0.5 = 0.105 \, \text{N m} \).

0.105 N m
0.12 N m
0.15 N m
0.18 N m
1

A bar magnet with original \( m = 3.0 \, \text{A m}^2 \) is cut along its length into two equal parts. What is \( m \) of each part?

When cut along its length, each part typically has half the original magnetic moment in standard problems.

Given: \( m = 3.0 \, \text{A m}^2 \).

Each part: \( m' = \frac{3.0}{2} = 1.5 \, \text{A m}^2 \).

1.2 A m²
1.3 A m²
1.4 A m²
1.5 A m²
4

Which material exhibits perfect diamagnetism with \( \chi = -1 \) and is used in levitating trains?

Superconductors exhibit perfect diamagnetism with \( \chi = -1 \) due to the Meissner effect and are used in applications like magnetically levitated trains.

Diamagnetic
Paramagnetic
Superconductor
Ferromagnetic
3

A material placed in a magnetic field reduces the field inside it slightly due to:

Diamagnetic materials reduce the magnetic field inside them slightly because an external field induces weak currents that create an opposing magnetic moment, resulting in a small negative susceptibility and a minor field reduction.

Induced opposing magnetic moments
Alignment of atomic dipoles
Formation of magnetic domains
Complete expulsion of the field
1

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