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Electricity and Magnetism

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Moderate

Farady-Voltage induced in a Circular Loop vs. Square Loop

EANDM-HS559N

A circular coil is formed from 2 loops, or turns, of wire. This coil is placed in a magnetic field such that its normal to the area defined by the loops is parallel to the direction of the magnetic field. The magnetic field is changing at a specific rate, and the voltage induced at the ends of the wire is measured to be $V_{circle}$.

The wire forming the circular coil is then unwound, and the entire length of wire is then formed into a square coil, with only one turn. The normal of the square coil is also parallel to the magnetic field. The magnetic is again changing at the same rate as with the circular coil, and the voltage $V_{square}$ is measured.

What is the ratio of voltage induced in the square to the voltage induced in the circular coil, $\cfrac{V_{square}}{V_{circle}}$?

A

$\cfrac{V_{square}}{V_{circle}}=\cfrac{\pi}{8}$

B

$\cfrac{V_{square}}{V_{circle}}=\cfrac{\pi}{2}$

C

$\cfrac{V_{square}}{V_{circle}}=\pi$

D

$\cfrac{V_{square}}{V_{circle}}=1$