Around flat metal coil has 180 turns and negligible resistance. it is connected in a series circuit with a 17-ω resistor, with nothing else in the circuit. you measure that a 6.0-a current flows through the resistor when a magnetic field through the coil, perpendicular to its area, is changing at 3.0 t/s. what is the radius of the coil?

(a) 0.043 m
(b) 0.014 m
(c) 0.25 m
(d) 0.54 m

C) 0.25 m

Explanation: In order to explain this problem we have to consider the Faraday law, we have:

ε=-dФ/dt where ε the emf induced by the change of the magnetic field given by dФ/dt.

then ε=I*R=17*6=102 V

We have a coil then we have the magnetic flux as follow:

Ф=N*A*B then we have

dФ/dt= N*A*dB/dt  where A and N is the area and number of turn of the coil.

A=π*R^2 where R is the radius of teh coil.

Finally we have;

dФ/dt= N*π*R^2*dB/dt then

R= [dФ/dt/(N*π*dB/dt)]^1/2= [102/(180*π*3)]1/2=245.2*10^-3=≅0.25m