A long solenoid with 1.30 times 10^3 turns per meter and radius 2.00 cm carries

Question

A long solenoid with 1.30 times 10^3 turns per meter and radius 2.00 cm carries an oscillating current I = 8.00 sin 90 pi t, where I is in amperes and t 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 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

Explanation / Answer

A). The induced Emf = µo*n*A*dI/dt where A = area of the 1cm loop = *r^2

so E = Emf/2r

or E = ( µo*n*A*dI/dt/2r)

now dI/dt = 90*7*cos(90t)

so E = µo*1300**r^2*90*7*cos(90t)/2r

simplifying 2.0*10^-7*1300*^2*0.010*90*7*cos(90t) = 1.615*10^-2*cos(90t) V/m

so E = 16*cos(120t) mV/m

B). Clockwise

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