A circular area with a radius of 7.00 cm lies in the x y -plane. Q1: What is the

Question

A circular area with a radius of 7.00 cm lies in the xy-plane.

Q1: What is the magnitude of the magnetic flux through this circle due to a uniform magnetic field with a magnitude of 0.300 T in the + z -direction?

Q2: What is the magnitude of the magnetic flux through this circle due to the same magnetic field (with a magnitude of 0.300 T ), now at an angle of 50.0 from the   + z -direction?

Q3: What is the magnitude of the magnetic flux through this circle due to the same magnetic field (with a magntiude of 0.300 T ), now in the + y -direction?

Explanation / Answer

1)

The xy plane is perpendicular to the z axis meaning the flux is perpendicular to the xy plane

The magnetic flux = (magnetic field intensity)(area)cos(theta)

In this case theta = 0

The magnetic flux = 0.300 wb/m^2 x [pi*(0.07 m)^2] x cos(0)

The magnetic flux = 0.00462 Wb

2)

In this case, theta = 50 degree

The magnetic flux =  0.00462 Wb x cos(50)

The magnetic flux = 0.00297 Wb

3)

theta = 90 degree

The magnetic flux =  0.00462 Wb x cos(90)

The magnetic flux = 0 Wb

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