A long solenoid with 1.95 times 10^2 turns per meter and radius 2.00 cm carries

Question

A long solenoid with 1.95 times 10^2 turns per meter and radius 2.00 cm carries an oscillating current t = 7.00 sin 12 O pi t, where I is in amperes and is in seconds. (a) What is the electric field induced at a radius r = 1.00 cm from the axis of the solenoid? (Use the following as necessary t. Let E be measured in millivolts/meter and t be measured in seconds.) E = (b) What is the direction of this electric field when the current is increasing counterclockwise in the solenoid? clockwise counterclockwise In a 280-turn automobile alternator, the magnetic flux in each turn is Phi_B = 2.50 times 10^-4 cos wt, where Phi_B is in webers, omega is the angular speed of the alternator, and t is in seconds. The alternator is geared to rotate six times for each engine revolution. The engine is running at an angular speed of 1.00 times 10^3 rev/min. (a) Determine the induced emf in the alternator as a function of time. (Assume epsilon is in V.) epsilon = (b) Determine the maximum emf in the alternator.

Explanation / Answer

EMF = -N*d(phi)/dt

EMF = -N*d(2.5*10^-4*cos wt)/dt

EMF = +w*N*2.5*10^-4*sin wt

w = 2*pi*f

f = 6*f0

f = 6*1000 rev/min = 6000 rev/min = 60 rev/sec

w = 2*pi*60 = 120*pi

EMF = 120*280*pi*2.5*10^-4*sin (120*pi*t)

EMF = 26.39*sin (120*pi*t)

B.

max EMF will be when sin wt = 1

then

EMF)max = 26.39 V

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