A circular loop of wore with radius 5.0 cm and 50 turns lies in the x-y plane. A

Question

A circular loop of wore with radius 5.0 cm and 50 turns lies in the x-y plane. A time varying field fills space.
Please answer a,b, c and d
Homework Problem 10.17 A circular loop of wire with ra- dius 5.0cm and 50turns lies in the z-y plane. A time varying magnetic field fills space, B 5.0 x 10-6t3(T/s3)2. Loop (a)Compute the magnetic flux as a function of time. (b)Compute the induced EMF at t = 10s. (c)Sketch the direction of the induced current. Explain why you selected this direction. (d)lf the field is generated by a source with current 3t3 A/s3, what is the mutuaHinductance between the source and the loop? Magnetic Field Out of Paper

Explanation / Answer

a)

magnetic flux phi = N*B*A

A = area of circle = pi*r^2

N = number of loops

phi = N*B*pi*r^2

phi = 50*5*10^-6*t^3*pi*0.05^2

phi = 1.96*10^-6 t^3 wb

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(b)

induced emf = rate of change in flux

emf = 1.96*10^-6*3*t^2

emf = 5.88*10^-6*t^2

at time t = 10 s

emf = 5.88*10^-6*10^2 = 5.88*10^-4 V

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(c)

magnetic field increases outwards

induced emf always opposes the change in flux

induced magentic field is inwards

by right hand rule the indcuced current is clockwise

CLOCKWISE

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(d)

magnetic flux phi = M*I

Mutual inductance M = phi/I

M = 1.96*10^-6 t^3/3t^3

M = 0.65*10^-6 H

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