At the equator, the direction of Earth\'s magnetic field is horizontal and to th

Question

At the equator, the direction of Earth's magnetic field is horizontal and to the north, and the magnitude is 3.5 ×105T.

Part A

What is the magnetic flux through a circular loop of radius 0.12 m , lying flat on the ground at the equator?

Part B

What is the magnetic flux through the loop of radius 0.12 m balanced on its edge on the ground at the equator, when the axis that runs perpendicular to the plane of the loop points northwest?

Part C

What is the magnetic flux through the loop of radius 0.12 m balanced on its edge on the ground at the equator, when the axis that runs perpendicular to the plane of the loop is points due north?

Part D

What is the magnetic flux through the loop of radius 0.12 m balanced on its edge on the ground at the equator, when the axis that runs perpendicular to the plane of the loop is points to the west?

All units expressed as Wb

Explanation / Answer

A) magnetic field is horizontal.

and area vector of coil is vertcial.
and flux = B.A    (dot product)

    = |B||A|cos@

here @ = 90 deg

hence flux = 0

B) now @ = 45 deg

flux = (3.5 x 10^-5) ( pi x 0.12^2) cos45 = 1.12 x 10^-6 T

C) @ = 0 deg

flux = (3.5 x 10^-5) ( pi x 0.12^2) cos0 = 1.58 x 10^-6 T

D) @ = 90

hence flux = 0

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