A circular area with a radius of 7.40 cm lies in the x-y plane. A.) What is the

Question

A circular area with a radius of 7.40 cm lies in the x-y plane.

A.) What is the magnitude of the magnetic flux through this circle due to a uniform magnetic field B = 0.246 T that points in the +z direction? (units are Wb).

B.) What is the magnitude of the magnetic flux through this circle due to a uniform magnetic field B = 0.246 T that points at an angle of 53.2 from the +z direction? (units are Wb)

C.) What is the magnitude of the magnetic flux through this circle due to a uniform magnetic field B = 0.246 T that points in the +y direction? (Units are Wb)

Explanation / Answer

A) magnetic flux = B . A   (dot product)

A = pi x 0.074^2 k = 0.0172 m^2 k

B = 0.246 T k

Flux = (0.246k)(0.0172k) = 4.232 x 10^-3 Wb

B) flux = B.A = |B||A| cos@

where @ is the angle between area vector and field vector.

@ = 53.2

flux = 4.323 x 10^-3 x cos53.2 = 2.535 x 10^-3 Wb

C) B = 0.246 T j

A = 0.0172 m^2 k

flux = B.A = (0.246 j) . (0.0172k) = 0

Or @ = 90 deg

and cos 90 = 0

so flux = 0

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