Question

A conducting circular loop made of a thin wire, has area 3.510-3m2 and resistance 10. It is placed perpendicular to a time dependent magnetic field b(t)=(0.4t)sin(50t). The field is uniform in space. Then the net charge flowing through the loop during t = 0 s and t = 10 ms is close to:

Answer 1

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Answer 2

The net charge flowing through the loop is $\bold{140 \ \mu C}$

Given:

Area of the loop = $\bold{3.5 \times 10^{-3} \ m^2}$

Resistance of the wire = 10 Ω

Magnetic field = B(t) = $\bold{(0.4T) sin(50\pi t)}$

To find:

Net charge from 0 s to 10 ms = ?

Formula:

$\bold{Q = \frac{\Delta \phi}{R}}$

Where,

Δϕ = Change in Current

R = Resistance

Solution:

$\bold{Q = \frac{\Delta \phi}{R}}$

$\bold{Q = \frac{ 1}{R} (B_r - B_i) A}$

$\bold{Q = \frac{ 1}{10} (0.4 \sin(50\pi 0.01) - 0) \times 3.5 \times 10^{-3}}$

$\bold{Q = \frac{ 1}{10} (0.4 \sin(0.5\pi) - 0) \times 3.5 \times 10^{-3}}$

$\bold{Q = \frac{ 1}{10} (0.4 \sin(\frac{1}{2}\pi) - 0) \times 3.5 \times 10^{-3}}$

$\bold{Q = \frac{ 1}{10} (0.4 \sin\frac{\pi}{2} - 0) \times 3.5 \times 10^{-3}}$

$\bold{\because \sin \frac{\pi}{2} = 1 }$

$\bold{Q = \frac{ 1}{10} (0.4 - 0) \times 3.5 \times 10^{-3}}$

$\bold{Q = 1.4 \times 10^{-4} \ C}$

$\bold{\therefore Q = 140 \ \mu C}$