Question

A flat circular coil with 193 turns, a radius of 5.50 x 10-2 m, and a resistance of 0.241 Ω is exposed to an external magnetic field that is directed perpendicular to the plane of the coil. The magnitude of the external magnetic field is changing at a rate of ΔB/Δt = 0.908 T/s, thereby inducing a current in the coil. Find the magnitude of the magnetic field at the center of the coil that is produced by the induced current.

Answer 1

find induced EMF from 193 *area * dB/dt
E = (193)pi (5.5*10^-2)^2 (.908)

current = i = E/.241

now find B due to i
B = mu N i/2 r
= 4 pi*10^-7 (193)(i)/(2*5.5*10^-2)

Answer 2

I followed the above instructions but I kept getting the wrong answer. (My homework is online)

E=193(pi)(5.5E-2)^2(0.908)=1.6654
I=E/R=1.6654/0.241 ohms=6.9104 amps

B= (4pi E-7)(193) (6.9104) 2(5.5E-2)
B=1.8436 E-4

I redid the calculations multiple times and still got the wrong answer. Where am I going wrong?