Question

A circular conducting loop with a radius of 0.50 m and a small gap filled with a 10.0-Ω resistor is oriented in the xy-plane. If a uniform magnetic field of 1.0 T, making an angle of 30∘ with the z-axis, increases to 10.0 T, in 4.0 s, what is the magnitude of the current that will be caused to flow in the loop if it has negligible resistance?

Answer 1

Answer:

Current, I = 0.153 A

Explanation:

Given that,

Radius of the circular conducting loop, r = 0.5 m

Resistance of the resistor, $R=10\ \Omega$

Magnetic field, B = 1 T

Angle with z axis, $\theta=30^{\circ}$

Magnetic field increases to 10 T in 4 seconds

To find,

Magnitude of current.

Solve,

According to Faraday's law, the induced emf is given by:

$\epsilon=\dfrac{\phi_f-\phi_i}{t}$

$\phi_f\ and\ \phi_i$ are final flux and the initial flux respectively.

$\epsilon=NA\ cos\theta\dfrac{B_f-B_i}{t}$

$\epsilon=1\times \pi (0.5)^2\ cos(30)\dfrac{10-1}{4}$

$\epsilon=1.53\ V$

The magnitude of current can be calculated using the Ohm's law as :

$I=\dfrac{\epsilon}{R}$

$I=\dfrac{1.53}{10}$

I = 0.153 A

Therefore, the magnitude of the current that will be caused to flow in the loop is 0.153 A.