GOAL Calculate magnetic flux and a change in flux PROBLEM A conducting circular

Question

GOAL Calculate magnetic flux and a change in flux PROBLEM A conducting circular loop of radius 0250 m is placed in the r-plane in a uniform magnetic field of 0.360 T that poits in the positive -direction, the same direction as the normal to the plane. (a) Calculate the magnetic flux through the loop. (b) Suppose the loop is rotated clockwise around the r-axis, so the normal direction now points at a 45.0° angle with respect to the a-axis. Recaliculate the magnetic flux through the loop. (e) What is the change in flux due to the rotation of the loop? STRATEGY After finding the area, substitute values into the equation for magnetic flux for each part. Because the normal direction was chosen to be the same direction as the magnetic field, the angle between the magnetic field and the normal is ntially 0. After the rotation, that angle becomes 45 (a) Calculate the initial magnetic flux through the loop. (b) Calculate the magnetic flux through the loop after it has rotated 45.0 around the -axis. (c) Find the change in the magnetic flux due to the rotation of the loop. REMARKS Notice that the rotation of the loop, not any change in the magnetic field, is responsible for the change in nux. This changing magnetic flu essential in the functioning of electric motors and generators QUESTION If the loop is rotated in the opposite direction by the same amount, which change in magnetic flux is true? Consider how the flux depends on angle 6 in the equation below and in the example. What is the initial value of e in the example? How do the magnitude and sign of the change in flux n the equation below compare if the change is made in the opposite direction? The loop, having rotated by 45, rotates clockwise another 30,so that the normal to the plane points at an angle of 75 with respect to the direction of the magnetic field (a) Find the magnetic flux through the loop when e 75.. (b) Find the change in magnetic flux during the rotation from 45 to 75*

Explanation / Answer

1.

It has the same magnitude

and It has the same sign

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Area of loop

A=pi*0.252 =0.19635 m2

Magnetic flux

phi=BACos(75) =0.36*0.19635*Cos75=0.0183 Wb

b)

Magnetic flux

dphi=BA(Cos75-Cos45)

dph =(0.36)(0.19635)*(Cos75-Cos45)

dph=-0.0316 Wb

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