A 12-cm-diameter circular loop of wire is placed in a 0.74-T magnetic field. Par

Question

A 12-cm-diameter circular loop of wire is placed in a 0.74-T magnetic field.

Part A When the plane of the loop is perpendicular to the field lines, what is the magnetic flux through the loop? Express your answer to two significant figures and include the appropriate units.

Part B The plane of the loop is rotated until it makes a 38? angle with the field lines. What is the angle in the equation ?B = BAcos?for this situation? Express your answer using two significant figures.

Part C What is the magnetic flux through the loop at this angle? Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

Given that

B = 0.74 T

d = 12 cm

r = 12 cm / 2 = 6 cm = 0.06 m

Part A

When the plane of the loop is perpendicular, then the magnetic flux passing through the loop is

Magnetic flux = B . A cos@

= B A cos0 [ where @ is the angle between normal to the loop and magnetic field , @ = 90 - 90 = 0 deg]

= BA

= B * pi * r2

= 0.74 x 3.14 * 0.062

= 0.00836496 Wb

Part B

If the plane of the loop rotated through 38 deg, then

@ = 90 - 38 = 52.00 deg

Part C

The magentic flux through the loop when it is rotated through 38 deg

magnetic flux = B A cos52

   = B * pi * r2 * cos52

= 0.74 x 3.14 * 0.062 * cos52

     = 0.00514998 Wb

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