Moving Charge and Magnetism Chapter-Wise Test 7

Correct answer Carries: 4.

Wrong Answer Carries: -1.

A wire of length \( 1.7 \, \text{m} \) carrying \( 7 \, \text{A} \) is at \( 60^\circ \) to a magnetic field of \( 0.2 \, \text{T} \). What is the force on the wire?

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

\( F = 7 \times 1.7 \times 0.2 \times \sin 60^\circ = 2.38 \times 0.866 = 2.061 \approx 2.06 \, \text{N} \).

1.19 N
2.38 N
1.73 N
2.06 N
4

A solenoid with 2500 turns per meter carries a current of \( 2 \, \text{A} \). What is the magnetic field inside it? (\( \mu_0 = 4 \pi \times 10^{-7} \, \text{T m/A} \))

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

\( B = 4 \pi \times 10^{-7} \times 2500 \times 2 = 20 \pi \times 10^{-4} \approx 6.28 \times 10^{-3} \, \text{T} \).

6.28 × 10⁻³ T
3.14 × 10⁻³ T
1.57 × 10⁻³ T
9.42 × 10⁻³ T
1

A straight wire of length \( 1.5 \, \text{m} \) carries a current of \( 6 \, \text{A} \) perpendicular to a uniform magnetic field of \( 0.25 \, \text{T} \). What is the force on the wire?

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

\( F = 6 \times 1.5 \times 0.25 = 2.25 \, \text{N} \).

2.25 N
4.5 N
1.13 N
3.38 N
1

A straight wire of length \( 1.4 \, \text{m} \) carries a current of \( 3 \, \text{A} \) perpendicular to a uniform magnetic field of \( 0.35 \, \text{T} \). What is the force on the wire?

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

\( F = 3 \times 1.4 \times 0.35 = 1.47 \, \text{N} \).

1.47 N
2.94 N
0.74 N
1.05 N
1

A solenoid with 1600 turns per meter carries a current of \( 2 \, \text{A} \). What is the magnetic field inside it? (\( \mu_0 = 4 \pi \times 10^{-7} \, \text{T m/A} \))

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

\( B = 4 \pi \times 10^{-7} \times 1600 \times 2 = 12.8 \pi \times 10^{-4} \approx 4.02 \times 10^{-3} \, \text{T} \).

4.02 × 10⁻³ T
2.01 × 10⁻³ T
8.04 × 10⁻³ T
6.03 × 10⁻³ T
1

A rectangular loop of area \( 0.08 \, \text{m}^2 \) with 15 turns carries \( 2.5 \, \text{A} \) in a field of \( 0.6 \, \text{T} \) at \( 30^\circ \) to the plane. What is the torque?

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

\( \tau = 15 \times 2.5 \times 0.08 \times 0.6 \times \sin 30^\circ = 1.8 \times 0.5 = 0.9 \, \text{N m} \).

1.56 N m
0.52 N m
0.9 N m
1.2 N m
3

What is the primary function of the shunt resistance in converting a galvanometer to an ammeter?

A shunt resistance is connected in parallel with the galvanometer to allow most of the current to bypass it, reducing the effective resistance and enabling the measurement of larger currents.

Increase sensitivity
Increase resistance
Reduce sensitivity
Bypass excess current
4

A circular loop of radius \( 0.14 \, \text{m} \) with 15 turns carries a current of \( 4 \, \text{A} \). What is the magnetic field at the center? (\( \mu_0 = 4 \pi \times 10^{-7} \, \text{T m/A} \))

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

\( B = \frac{4 \pi \times 10^{-7} \times 15 \times 4}{2 \times 0.14} = \frac{24 \pi \times 10^{-6}}{0.28} = \frac{6 \pi}{7} \times 10^{-5} \approx 2.69 \times 10^{-4} \, \text{T} \).

1.35 × 10⁻⁴ T
2.69 × 10⁻⁴ T
5.38 × 10⁻⁴ T
4.04 × 10⁻⁴ T
2

A rectangular loop of area \( 0.05 \, \text{m}^2 \) with 15 turns carries \( 2 \, \text{A} \) in a field of \( 1 \, \text{T} \) at \( 90^\circ \) to the plane. What is the torque?

\( \tau = N I A B \sin \theta \), \( \theta = 90^\circ \) to plane means \( \sin 0^\circ = 1 \) with normal.

\( \tau = 15 \times 2 \times 0.05 \times 1 \times 1 = 1.5 \, \text{N m} \).

0.75 N m
3 N m
1 N m
1.5 N m
4

A long wire carries \( 16 \, \text{A} \). At what distance is the magnetic field \( 8 \times 10^{-6} \, \text{T} \)? (\( \mu_0 = 4 \pi \times 10^{-7} \, \text{T m/A} \))

\( B = \frac{\mu_0 I}{2 \pi r} \), so \( r = \frac{\mu_0 I}{2 \pi B} \).

\( r = \frac{4 \pi \times 10^{-7} \times 16}{2 \pi \times 8 \times 10^{-6}} = \frac{64 \times 10^{-7}}{16 \times 10^{-6}} = 0.4 \, \text{m} \).

0.2 m
0.8 m
0.4 m
1.2 m
3

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