A circular conducting coil with radius 3.20 cm is placed in a uniform magnetic f

Question

A circular conducting coil with radius 3.20 cm is placed in a uniform magnetic field of 1.070 T with the plane of the coil perpendicular to the magnetic field as shown. The coil is rotated 180 about the axis in 0.222 s.

(a) What is the average induced emf in the coil during this rotation?
mV

(b) If the coil is made of copper with a diameter of 0.900 mm, what is the average current that flows through the coil during the rotation?
A

A circular conducting coil with radius 3.20 cm is placed in a uniform magnetic field of 1.070 T with the plane of the coil perpendicular to the magnetic field as shown. The coil is rotated 180 about the axis in 0.222 s. (a) What is the average induced emf in the coil during this rotation? mV (b) If the coil is made of copper with a diameter of 0.900 mm, what is the average current that flows through the coil during the rotation? A

Explanation / Answer

The average induced emf is the time rate of change in flux ;

V = [BACos(@f) - BACos(@i)]/t

where "@" is the angle between the direction of "B" & "A". This angle changes when the coil is flipped because the direction of "A" changes;

@i = 0 deg
@f = 180 deg

V = [BA(1) - BA(-1)]/t
= 2BA/t
= (2)(1.07)(pi)(.032)^2/.222
= .030994 v
= 30.994 mv

I assume you can now do part (b) using;

V = iR
= i(pL/A)
= i(p2pir)/(piD^2/4)

You'll have to look up the resistivity "p" of Copper.

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