?

Electricity and Magnetism

Free Version

Upgrade subject to access all content

Difficult

Faraday--Coil at an Angle in a Magnetic Field

EANDM-UBE3KU

A flat coil of wire has 20 turns with a radius of $r_o$ is placed in a constant magnetic field $B_o$ such that the normal to its area is at an unknown angle, $\theta$, relative to the direction of the magnetic field. The coil has a total resistance of $R_o $. During a time interval of $\Delta T$ the magnetic field is increased at a constant rate from $B_0$ to $B_1$. During this interval of time, the current in the coil is measured to be $I_o$.

What is the angle, $\theta$, between the normal of the coils?

A

$\theta = cos^{-1} \bigg[ \cfrac{I_o R \, \Delta T}{20 (\pi r_o ^2) (B_1-B_0)} \bigg]$

B

$\theta = cos^{-1} \bigg[ \cfrac{I_o R }{20 (\pi r_o ^2) (B_1-B_0)} \bigg]$

C

$\theta = cos^{-1} \bigg[\cfrac{20 (\pi r_o^2)(B_1 - B_0)} {I_o R \,\Delta T }\bigg]$

D

$\theta = cos^{-1} \bigg[ \cfrac{I_o R \, \Delta T}{20 (B_1-B_0)} \bigg]$