3. A coil with N loops and radius R is surrounds a very long solenoid of radius

Question

3. A coil with N loops and radius R is surrounds a very long solenoid of radius r and n turns per meter.


The current in the solenoid is varying sinusoidally with time according to the relation I(t)=I0sin(2ft)

where I0 is the maximum value of the current, and f is its frequency. (This is the type of current supplied by the power company.) If R >> r, show that the induced emf in the coil is given by


=-2(^2)0fNn(r^2)I0cos(2ft)



--------------------------------------------------------------------------------

Explanation / Answer

magnetic field B = 0nI

magnetic flux = NB*r2

emf = -d/dt = -Nr2dB/dt = -Nr20dI/dt = -Nr20d[I0sin(2ft)]/dt

= -Nr20I02fcos(2ft) = -220fNnr2I0cos(2ft)

Related Questions

Navigate

• Browse (All)
• Browse 3
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.