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

The magnitude of the current is 5.45 mA.

Step-by-step 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*1.0*\pi*(0.10)^2*\cos30^(\circ)`

`\phi=1*1.0*\pi*(0.10)^2*(√(3))/(2)`

`\phi=0.027\ wb`

We need to calculate the final flux

`\phi=1*7.0*\pi*(0.10)^2*(√(3))/(2)`

`\phi=0.1904\ wb`

We need to calculate the induced emf

Using formula of emf

`\epsilon=(\phi_(f)-\phi_(i))/(t)`

Put the value into the formula

`\epsilon=(0.1904-0.027)/(3.0)`

`\epsilon=0.0545\ V`

We need to calculate the current

Using formula of current

`I=(\epsilon)/(R)`

Put the value into the formula

`I=(0.0545)/(10.0)`

`I=5.45\ mA`

Hence, The magnitude of the current is 5.45 mA.