Homework Problem 10.17 A circular loop of wire with ra- dius 5.0cm and 50turns l

Question

Homework Problem 10.17 A circular loop of wire with ra- dius 5.0cm and 50turns lies in the r-y plane. A time varying magnetic field fills space, L = 5.0 × 10-613(T/s3)2. Loop (a)Compute the magnetic flux as a function of time. (b)Compute the induced EMF at 1 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 3t3A/s". what is the mutual inductance between the source and the loop? Magnetic Field Out of Paper

Explanation / Answer

(A) magnetic flux = N B A

= 50 (pi 0.05^2) (5 x 10^-6 t^3)

= (1.96 x 10^-6) t^3

(b) induced emf = d(flux)/dt = 5.89 x 10^-6 t^2

at t = 10 s

e = 0.59 x 10^-3 Volt

(c) field is increasing out of page .

hence induced current will be clockwise.

(d) e2 = M d(flux1)/dt

3 t^2 R = (5.89 x 10^-6 t^2) M

M = (5.09 x 10^5) R

where R is resistance of coil.

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