Question

A circular conducting loop with a radius of 0.10 m and a small gap filled with a 10.0 ȍresistor is oriented in the xy-plane. If a magnetic field of 1.0 T, making an angle of 30°with the z-axis, increases to 7.0 T, in 3.0 s, what is the magnitude of the current thatwill be caused to flow in the conductor

Answer 1

Answer:

The magnitude of the current is 5.45 mA.

Explanation:

Given that,

Resistance = 10.0 ohm

Radius = 0.10 m

Magnetic field = 1.0 T

Angle = 30°

Increase magnetic field = 7.0 T

Time t = 3.0 s

Number of turns = 1

We need to calculate the initial flux

Using formula of flux

$\phi=NB_{1}A\cos\theta$

Put the value into the formula

$\phi=1\times1.0\times\pi\times(0.10)^2\times\cos30^{\circ}$

$\phi=1\times1.0\times\pi\times(0.10)^2\times\dfrac{\sqrt{3}}{2}$

$\phi=0.027\ wb$

We need to calculate the final flux

$\phi=1\times7.0\times\pi\times(0.10)^2\times\dfrac{\sqrt{3}}{2}$

$\phi=0.1904\ wb$

We need to calculate the induced emf

Using formula of emf

$\epsilon=\dfrac{\phi_{f}-\phi_{i}}{t}$

Put the value into the formula

$\epsilon=\dfrac{0.1904-0.027}{3.0}$

$\epsilon=0.0545\ V$

We need to calculate the current

Using formula of current

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

Put the value into the formula

$I=\dfrac{0.0545}{10.0}$

$I=5.45\ mA$

Hence, The magnitude of the current is 5.45 mA.