A solenoid has 240 turns/cm and a radius of 1.5 cm. It carries an initial consta

Question

A solenoid has 240 turns/cm and a radius of 1.5 cm. It carries an initial constant current of 1.5 Amps in the clockwise direction when seen end-on (cutaway on left, end-on view on right). The solenoid is coaxial with a coil of wire of radius 1.8 cm, 350 turns and a total resistance of 2.7 Ohms. a) If the current in the solenoid drops from 1.5 A to zero in a time interval of 0.025 seconds, what is the magnitude and direction (seen end-on) of the induced current in the coil? b) If the current in the solenoid starts at zero and increases to 1.5 A in a counterclockwise direction in 0.025 seconds, what is the magnitude and direction of the induced current in the coil?

Explanation / Answer

part(a)

magnetic field inside a solenoid B = uo*n*I

n = 240 turns/cm = 24000 turns /m

radius of coil r1 > r

r = 1.5 cm

magnetic flux through coil = N*B*A

A = area of cross ection = pi*r^2

emf = rate of change in flux E = N*(dB/dt)*A

E = N*uo*n*A*(dI/dt) = -350*4*pi*10^-7*24000*pi*0.015^2*(0-15)/(0.025)

E = 4.48 V

induced current I = E/R = 4.48/2.7 = 1.66 A <<<<=======answer

direction clockwise   <<<=======answer

================

(b)

emf = rate of change in flux E = N*(dB/dt)*A

E = N*uo*n*A*(dI/dt) = -350*4*pi*10^-7*24000*pi*0.015^2*(0-15)/(0.025)

E = 4.48 V

induced current I = E/R = 4.48/2.7 = 1.66 A <<<<=======answer

direction clockwise   <<<=======answer

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