Moving Charge and Magnetism Chapter-Wise Test 8

Correct answer Carries: 4.

Wrong Answer Carries: -1.

A solenoid has 700 turns per meter and carries a current of \( 2.8 \, \text{A} \). What is the magnetic field inside it? (\( \mu_0 = 4 \pi \times 10^{-7} \, \text{T m/A} \))

Magnetic field \( B = \mu_0 n I \).

\( B = 4 \pi \times 10^{-7} \times 700 \times 2.8 = 7.84 \pi \times 10^{-4} \approx 2.46 \times 10^{-3} \, \text{T} \).

1.23 × 10⁻³ T
2.46 × 10⁻³ T
4.92 × 10⁻³ T
3.69 × 10⁻³ T
2

Two parallel wires \( 0.03 \, \text{m} \) apart carry currents of \( 10 \, \text{A} \) and \( 2 \, \text{A} \) in the same direction. What is the force per unit length between them? (\( \mu_0 = 4 \pi \times 10^{-7} \, \text{T m/A} \))

Force per unit length \( f = \frac{\mu_0 I_1 I_2}{2 \pi d} \).

\( f = \frac{4 \pi \times 10^{-7} \times 10 \times 2}{2 \pi \times 0.03} = \frac{80 \times 10^{-7}}{0.06} = 1.333 \times 10^{-5} \approx 1.33 \times 10^{-5} \, \text{N/m} \).

6.67 × 10⁻⁶ N/m
1.33 × 10⁻⁵ N/m
2.67 × 10⁻⁵ N/m
2.00 × 10⁻⁵ N/m
2

A straight wire of length \( 0.9 \, \text{m} \) carries a current of \( 7 \, \text{A} \) perpendicular to a uniform magnetic field of \( 0.2 \, \text{T} \). What is the force on the wire?

Force \( F = I l B \sin \theta \), where \( \theta = 90^\circ \), so \( \sin \theta = 1 \).

\( F = 7 \times 0.9 \times 0.2 = 1.26 \, \text{N} \).

1.26 N
2.52 N
0.63 N
1.8 N
1

A wire of length \( 1.6 \, \text{m} \) carrying \( 5 \, \text{A} \) is at \( 45^\circ \) to a magnetic field of \( 0.1 \, \text{T} \). What is the force on the wire?

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

\( F = 5 \times 1.6 \times 0.1 \times \sin 45^\circ = 8 \times 0.1 \times 0.707 = 0.5656 \approx 0.57 \, \text{N} \).

0.8 N
0.57 N
1.14 N
0.28 N
2

A wire of length \( 0.8 \, \text{m} \) carrying \( 3 \, \text{A} \) makes an angle of \( 30^\circ \) with a magnetic field of \( 0.6 \, \text{T} \). What is the force on the wire?

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

\( F = 3 \times 0.8 \times 0.6 \times \sin 30^\circ = 2.4 \times 0.6 \times 0.5 = 0.72 \, \text{N} \).

1.44 N
0.72 N
0.36 N
1.08 N
2

Two parallel wires \( 0.09 \, \text{m} \) apart carry \( 4 \, \text{A} \) and \( 5 \, \text{A} \) in opposite directions. What is the force per unit length? (\( \mu_0 = 4 \pi \times 10^{-7} \, \text{T m/A} \))

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

\( f = \frac{4 \pi \times 10^{-7} \times 4 \times 5}{2 \pi \times 0.09} = \frac{80 \times 10^{-7}}{0.18} = 4.44 \times 10^{-6} \, \text{N/m} \).

2.22 × 10⁻⁶ N/m
8.88 × 10⁻⁶ N/m
4.44 × 10⁻⁶ N/m
6.67 × 10⁻⁶ N/m
3

A long straight wire carries a current of \( 22 \, \text{A} \). What is the magnetic field at a distance of \( 0.2 \, \text{m} \) from it? (\( \mu_0 = 4 \pi \times 10^{-7} \, \text{T m/A} \))

Magnetic field \( B = \frac{\mu_0 I}{2 \pi r} \).

\( B = \frac{4 \pi \times 10^{-7} \times 22}{2 \pi \times 0.2} = \frac{88 \times 10^{-7}}{0.4} = 2.2 \times 10^{-5} \, \text{T} \).

2.2 × 10⁻⁵ T
4.4 × 10⁻⁵ T
1.1 × 10⁻⁵ T
3.3 × 10⁻⁵ T
1

A circular coil of radius \( 0.04 \, \text{m} \) with 50 turns carries \( 1.8 \, \text{A} \). What is the magnetic field at the center? (\( \mu_0 = 4 \pi \times 10^{-7} \, \text{T m/A} \))

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

\( B = \frac{4 \pi \times 10^{-7} \times 50 \times 1.8}{2 \times 0.04} = \frac{36 \pi \times 10^{-6}}{0.08} = 4.5 \pi \times 10^{-4} \approx 1.41 \times 10^{-3} \, \text{T} \).

7.07 × 10⁻⁴ T
2.82 × 10⁻³ T
1.06 × 10⁻³ T
1.41 × 10⁻³ T
4

A long straight wire carries a current of \( 30 \, \text{A} \). What is the magnetic field at a distance of \( 0.3 \, \text{m} \) from it? (\( \mu_0 = 4 \pi \times 10^{-7} \, \text{T m/A} \))

Magnetic field \( B = \frac{\mu_0 I}{2 \pi r} \).

\( B = \frac{4 \pi \times 10^{-7} \times 30}{2 \pi \times 0.3} = \frac{120 \times 10^{-7}}{0.6} = 2 \times 10^{-5} \, \text{T} \).

2 × 10⁻⁵ T
4 × 10⁻⁵ T
1 × 10⁻⁵ T
3 × 10⁻⁵ T
1

A solenoid with 900 turns per meter carries \( 2 \, \text{A} \). What is the magnetic field inside? (\( \mu_0 = 4 \pi \times 10^{-7} \, \text{T m/A} \))

\( B = \mu_0 n I \).

\( B = 4 \pi \times 10^{-7} \times 900 \times 2 = 7.2 \pi \times 10^{-4} \approx 2.26 \times 10^{-3} \, \text{T} \).

1.13 × 10⁻³ T
4.52 × 10⁻³ T
1.88 × 10⁻³ T
2.26 × 10⁻³ T
4

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