Question 1 please. A planar circular coil of wire with radius 14mm and N = 20 tu

Question

Question 1 please.

A planar circular coil of wire with radius 14mm and N = 20 turns sits in a uniform external magnetic field of magnitude 75mT. The area vector of the loop and the Magnetic field differ in direction by theta = 60 degree. A current of 4.0 Ampere flows through the loop. a) What is the magnetic moment of the loop? b) What is the magnetic torque on the loop due to the uniform external field? c) What is the magnetic flux through the loop (1 turn)? d) If the loop suddenly shifts to an angle of theta = 50 degree over 50 milliseconds, what is the average magnitude of EMF induced in the loop (All N turns)?

Explanation / Answer

1.(A) magnetic moment = N I A

= (20)(pi x (14 x 10^-3)^2) (4)

= 0.049 A m^2

(B) torque = u x B

= u B sin(theta)

= 0.049 x 0.075 x sin(60)

= 3.20 x 10^-3 N m

(C) flux = N ( B .A) = N B A cos(theta)

= 20 x 0.075 x pi x (0.014^2) cos60

= 4.62 x 10^-4 Wb

(D) induced emf = rate of change of flux

= (20 x 0.075 x pi x 0.014^2) (cos50 - cos60) / (50 x 10^-3)

= 2.64 x 10^-3 volt

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