Magnetic Effects Of Current And Magnetism Chapter-Wise Test 1

Correct answer Carries: 4.

Wrong Answer Carries: -1.

A long wire carries \( 14 \, \text{A} \). At what distance is the magnetic field \( 7 \times 10^{-6} \, \text{T} \)? (\( \mu_0 = 4 \pi \times 10^{-7} \, \text{T m/A} \))

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

\( r = \frac{4 \pi \times 10^{-7} \times 14}{2 \pi \times 7 \times 10^{-6}} = \frac{56 \times 10^{-7}}{14 \times 10^{-6}} = 0.4 \, \text{m} \).

0.2 m
0.8 m
0.4 m
1.2 m
3

A solenoid with 1400 turns per meter carries a current of \( 2.5 \, \text{A} \). What is the magnetic field inside it? (\( \mu_0 = 4 \pi \times 10^{-7} \, \text{T m/A} \))

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

\( B = 4 \pi \times 10^{-7} \times 1400 \times 2.5 = 14 \pi \times 10^{-4} \approx 4.40 \times 10^{-3} \, \text{T} \).

4.40 × 10⁻³ T
2.20 × 10⁻³ T
8.80 × 10⁻³ T
3.30 × 10⁻³ T
1

A wire of length \( 0.8 \, \text{m} \) carrying \( 5 \, \text{A} \) is at \( 30^\circ \) to a magnetic field of \( 0.8 \, \text{T} \). What is the force on the wire?

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

\( F = 5 \times 0.8 \times 0.8 \times \sin 30^\circ = 4 \times 0.8 \times 0.5 = 1.6 \, \text{N} \).

0.8 N
1.6 N
3.2 N
2.4 N
2

A circular coil of 45 turns and radius \( 6 \, \text{cm} \) carries a current of \( 1.2 \, \text{A} \). What is the magnetic field at its center? (\( \mu_0 = 4 \pi \times 10^{-7} \, \text{T m/A} \))

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

\( B = \frac{4 \pi \times 10^{-7} \times 45 \times 1.2}{2 \times 0.06} = \frac{21.6 \pi \times 10^{-6}}{0.12} = 1.8 \pi \times 10^{-4} \approx 5.65 \times 10^{-4} \, \text{T} \).

5.65 × 10⁻⁴ T
2.83 × 10⁻⁴ T
1.13 × 10⁻³ T
8.48 × 10⁻⁴ T
1

A circular loop of radius \( 0.08 \, \text{m} \) with 60 turns carries a current of \( 0.75 \, \text{A} \). What is the magnetic field at the center? (\( \mu_0 = 4 \pi \times 10^{-7} \, \text{T m/A} \))

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

\( B = \frac{4 \pi \times 10^{-7} \times 60 \times 0.75}{2 \times 0.08} = \frac{18 \pi \times 10^{-6}}{0.16} = 1.125 \pi \times 10^{-4} \approx 3.53 \times 10^{-4} \, \text{T} \).

1.77 × 10⁻⁴ T
3.53 × 10⁻⁴ T
7.06 × 10⁻⁴ T
5.30 × 10⁻⁴ T
2

A long wire carries \( 15 \, \text{A} \). At what distance is the magnetic field \( 3 \times 10^{-6} \, \text{T} \)? (\( \mu_0 = 4 \pi \times 10^{-7} \, \text{T m/A} \))

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

\( r = \frac{4 \pi \times 10^{-7} \times 15}{2 \pi \times 3 \times 10^{-6}} = \frac{60 \times 10^{-7}}{6 \times 10^{-6}} = 1 \, \text{m} \).

0.5 m
2 m
1 m
1.5 m
3

Which property of magnetic field lines distinguishes them from electric field lines?

Magnetic field lines form closed loops because there are no magnetic monopoles, unlike electric field lines, which originate from positive charges and terminate at negative charges or extend to infinity.

They are straight
They diverge from a point
They are always radial
They form closed loops
4

A square loop of side \( 0.15 \, \text{m} \) with 50 turns carries \( 1 \, \text{A} \) in a magnetic field of \( 0.6 \, \text{T} \). The plane of the loop is at \( 30^\circ \) to the field. What is the torque?

Torque \( \tau = N I A B \sin \theta \), where \( A = 0.15 \times 0.15 = 0.0225 \, \text{m}^2 \).

\( \tau = 50 \times 1 \times 0.0225 \times 0.6 \times \sin 30^\circ = 0.675 \times 0.5 = 0.3375 \approx 0.34 \, \text{N m} \).

0.17 N m
0.34 N m
0.68 N m
1.02 N m
2

Two parallel wires \( 0.08 \, \text{m} \) apart carry currents of \( 5 \, \text{A} \) and \( 3 \, \text{A} \) 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 \( f = \frac{\mu_0 I_1 I_2}{2 \pi d} \).

\( f = \frac{4 \pi \times 10^{-7} \times 5 \times 3}{2 \pi \times 0.08} = \frac{60 \times 10^{-7}}{0.16} = 3.75 \times 10^{-6} \, \text{N/m} \).

1.88 × 10⁻⁶ N/m
3.75 × 10⁻⁶ N/m
7.50 × 10⁻⁶ N/m
5.63 × 10⁻⁶ N/m
2

An electron moves at \( 7 \times 10^6 \, \text{m/s} \) perpendicular to a field of \( 0.2 \, \text{T} \). What is the magnetic force? (Charge = \( 1.6 \times 10^{-19} \, \text{C} \))

Force \( F = q v B \sin \theta \), \( \theta = 90^\circ \), so \( \sin \theta = 1 \).

\( F = 1.6 \times 10^{-19} \times 7 \times 10^6 \times 0.2 = 2.24 \times 10^{-13} \, \text{N} \).

1.12 × 10⁻¹³ N
4.48 × 10⁻¹³ N
2.24 × 10⁻¹³ N
3.36 × 10⁻¹³ N
3

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