Moving Charge and Magnetism Chapter-Wise Test 5

Correct answer Carries: 4.

Wrong Answer Carries: -1.

A wire of length \( 0.5 \, \text{m} \) carrying \( 4 \, \text{A} \) is placed at \( 60^\circ \) to a magnetic field of \( 0.3 \, \text{T} \). What is the force on the wire?

Force \( F = I l B \sin \theta \).

\( F = 4 \times 0.5 \times 0.3 \times \sin 60^\circ = 2 \times 0.3 \times 0.866 = 0.5196 \approx 0.52 \, \text{N} \).

0.3 N
0.52 N
0.6 N
0.9 N
2

A circular coil of 40 turns and radius \( 6 \, \text{cm} \) carries a current of \( 1 \, \text{A} \). What is the magnetic field at its center? (\( \mu_0 = 4 \pi \times 10^{-7} \, \text{T m/A} \))

Magnetic field \( B = \frac{\mu_0 N I}{2 R} \).

\( B = \frac{4 \pi \times 10^{-7} \times 40 \times 1}{2 \times 0.06} = \frac{16 \pi \times 10^{-6}}{0.12} = \frac{4 \pi}{3} \times 10^{-5} \approx 4.19 \times 10^{-5} \, \text{T} \).

4.19 × 10⁻⁵ T
8.38 × 10⁻⁵ T
2.09 × 10⁻⁵ T
6.28 × 10⁻⁵ T
1

A rectangular loop of area \( 0.04 \, \text{m}^2 \) with 18 turns carries \( 2.8 \, \text{A} \) in a field of \( 0.9 \, \text{T} \) at \( 60^\circ \) to the plane. What is the torque?

\( \tau = N I A B \sin \theta \), where \( \theta = 60^\circ \) to plane means \( \sin 30^\circ \) with normal.

\( \tau = 18 \times 2.8 \times 0.04 \times 0.9 \times \sin 60^\circ = 1.8144 \times 0.866 = 1.5712 \approx 1.57 \, \text{N m} \).

0.91 N m
3.14 N m
1.57 N m
2.36 N m
3

What is the direction of the magnetic field at the center of a circular current-carrying loop?

Using the right-hand rule, if the fingers curl along the direction of the current in the loop, the thumb points perpendicular to the plane of the loop, indicating the field direction at the center.

Parallel to the plane of the loop
Perpendicular to the plane of the loop
Along the radius of the loop
Zero at the center
2

Two parallel wires \( 0.08 \, \text{m} \) apart carry \( 7 \, \text{A} \) and \( 4 \, \text{A} \) in opposite directions. What is the force per unit length? (\( \mu_0 = 4 \pi \times 10^{-7} \, \text{T m/A} \))

\( f = \frac{\mu_0 I_1 I_2}{2 \pi d} \).

\( f = \frac{4 \pi \times 10^{-7} \times 7 \times 4}{2 \pi \times 0.08} = \frac{112 \times 10^{-7}}{0.16} = 7 \times 10^{-6} \, \text{N/m} \).

3.5 × 10⁻⁶ N/m
1.4 × 10⁻⁵ N/m
7 × 10⁻⁶ N/m
1.05 × 10⁻⁵ N/m
3

A wire of length \( 1 \, \text{m} \) with \( 10 \, \text{A} \) is at \( 45^\circ \) to a field of \( 0.2 \, \text{T} \). What is the force on it?

\( F = I l B \sin \theta \).

\( F = 10 \times 1 \times 0.2 \times \sin 45^\circ = 2 \times \frac{1}{\sqrt{2}} = 1.414 \approx 1.41 \, \text{N} \).

1 N
2 N
0.71 N
1.41 N
4

A solenoid with 1500 turns per meter carries \( 1.1 \, \text{A} \). What is the magnetic field inside? (\( \mu_0 = 4 \pi \times 10^{-7} \, \text{T m/A} \))

\( B = \mu_0 n I \).

\( B = 4 \pi \times 10^{-7} \times 1500 \times 1.1 = 6.6 \pi \times 10^{-4} \approx 2.07 \times 10^{-3} \, \text{T} \).

1.04 × 10⁻³ T
4.14 × 10⁻³ T
1.73 × 10⁻³ T
2.07 × 10⁻³ T
4

What happens to the magnetic field inside a solenoid when the current through it is doubled?

The magnetic field inside a solenoid is proportional to the current, given by \( B = \mu_0 n I \). If the current \( I \) is doubled, the magnetic field \( B \) also doubles.

It doubles
It halves
It remains unchanged
It becomes four times
1

A circular coil of radius \( 0.1 \, \text{m} \) with 20 turns carries \( 4 \, \text{A} \). What is the magnetic field at the center? (\( \mu_0 = 4 \pi \times 10^{-7} \, \text{T m/A} \))

\( B = \frac{\mu_0 N I}{2 R} \).

\( B = \frac{4 \pi \times 10^{-7} \times 20 \times 4}{2 \times 0.1} = \frac{32 \pi \times 10^{-6}}{0.2} = 16 \pi \times 10^{-5} \approx 5.03 \times 10^{-4} \, \text{T} \).

2.51 × 10⁻⁴ T
1.26 × 10⁻⁴ T
7.54 × 10⁻⁴ T
5.03 × 10⁻⁴ T
4

A solenoid with 2000 turns per meter carries \( 0.8 \, \text{A} \). What is the magnetic field inside? (\( \mu_0 = 4 \pi \times 10^{-7} \, \text{T m/A} \))

\( B = \mu_0 n I \).

\( B = 4 \pi \times 10^{-7} \times 2000 \times 0.8 = 6.4 \pi \times 10^{-4} \approx 2.01 \times 10^{-3} \, \text{T} \).

1.01 × 10⁻³ T
4.02 × 10⁻³ T
1.68 × 10⁻³ T
2.01 × 10⁻³ T
4

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