Question

A long solenoid with 1.65 103 turns per meter and radius 2.00 cm carries an oscillating current I = 7.00 sin 120?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 in millivolts/meter and t be measured in seconds.)

Answer 1

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

so E = Emf/2πr

or E = ( µo*n*A*dI/dt/2πr)

now dI/dt = 120π*7*cos(120πt)

so E = µo*1650*π*r^2*120π*7*cos(120πt)/2πr

simplifying 2.0x10^-7*1650*π^2*0.010*120*7*cos(120πt) = 2.7x10^-2*cos(120πt) V/m

so E = 27*cos(120πt) mV/m