(a) What is the electric field induced at a radius r = 1.00 cm from the axis of

Question

(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.)

A long solenoid with 9.50 x 102 turns per meter and radius 2.00 cm carries an oscillating current! = 3.00 sin 80 , 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.)

Explanation / Answer

Integration(E.dl) = -d(phi)/dt

Left side, Integration(E.dl) = E*2*r

Right side, For solenoid, B = uo*n*I

Phi = Integration(B.da) = B**r^2 = uo*n*I**r^2 = uo*n**r^2*(3.0*sin80t)

d(phi)/dt = 240*uo*n*^2*r^2*(cos80t)

Now E*2*r = 240*uo*n*^2*r^2*(cos80t)

E = 120*uo*n**r*(cos80t)

= 120*4**10^-7*950**0.01*(cos80t)

E = 4.5*10^-3*(cos80t) V/m

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