In this example, we use Phi = BA cos phi to solve for the strength of a magnetic

Question

In this example, we use Phi = BA cos phi to solve for the strength of a magnetic field. A plane surface with area 2.8 cm^2 is placed in a uniform magnetic field that is oriented at an angle of 30 degree to the surface, (a) What is the angle phi? (b) If the magnetic flux through this area is 0.96 mWb what is the magnitude of the magnetic field? SET UP AND SOLVE Part (a): (Figure 1) shows our sketch. As defined earlier, 0 is the angle between the direction of B and a line normal to the surface, so phi = 60 degree (not 30 degree). Part (b): Because B and phi are the same at all points on the surface, we can use Phi_B = BA cos phi. We solve for B, remembering to convert the area to square meters: B = Phi_B/A cos phi = 9.6 times 10^-4 Wb/(2.8 times 10^-4 m^2)(cos 60 degree) = 6.9 T REFLECT The flux through the surface depends on its angle relative to B. Knowing this angle and the flux per unit area, we can find the magnitude of the magnetic field. For the same B and A, find the angle phi at which the flux would have one half the value given above (i.e., the angle phi at which = 4.8 times 10^-4 Wb). Express your answer in degrees to two significant figures.

Explanation / Answer

Magnetic field strength (B) = 6.9 T

Area (A) = 2.8 cm2

the Flux has to be 4.8 x 10-4 Wb

so = BAcos

    4.8 x 10-4 = 6.9 x 2.8 x 10-4 cos

   4.8 / (6.9 x 2.8) = cos

   cos = 0.24844

= cos-1(0.24844)

= 75.610

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