The correct answer is shown in the photo, I\'m just not sure where my mistake is

Question

The correct answer is shown in the photo, I'm just not sure where my mistake is.

A long solenoid with 8.00 times 10^2 turns per meter and radius 2.00 cm carries an oscillating current I = 6.00 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 in mi volts/meter and t be measured in seconds.) (b) What is the direction of this electric field when the current is increasing counterclockwise in the solenoid? clockwise counterclockwise

Explanation / Answer

given

n = 8.0*10^2 turns/m

i = 6*sin(90*pi*t)

r = 1 cm

A = pi*r^2

= pi*0.01^2

= 3.14*10^-4 m^2

we know, magnetic field inside long solenoid, N = mue*n*I

now apply,

inetrgal E.dL = A*dB/dt

E*2*pi*r = pi*r^2*mue*n*6*cos(80*pi*t)*90*pi

E = 45*6*pi*r*mue*n*cos(80*pi*t)

= 45*6*pi*0.01*4*pi*10^-7*8.0*10^2*cos(90*pi*t)

= 8.51*10^-3*cos(90*pi*t) Volt/meter

= 8.51*cos(90*pi*t) milliVolt/meter------ans

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