Answer to Question #132835 in Electricity and Magnetism for Mr DB MAKATU

Question

a wire loop with radius 0.5 m and resistance 2 W is placed in a long solenoid with the plane of the loop perpendicular to the axis of the solenoid. The solenoid has a radius of 0.15 m and has 2500 turns per meter. A current is switched on inside the solenoid and reaches its maximum value in 0.02 s. If a current of 4 mA if induced in the loop, what is the maximum value of the current induced in the solenoid?

Answer 1

$Solution:\\ The \;current \ is\ induced\ in\ the\ loop\;I_i=\frac{ B}{ t}\times\frac{S}{R};\\Induction\ in\ the\ solenoid\;is\;B=\mu_0nI_{max},\\and\ then\ we\ get\\I{max}=\frac{I_itR}{\mu_0nS}=\frac{0.004\times0.02\times2}{1.26\times10^{-6}\times2500\times{\pi}\times0.5^2}=0.065A;\\Answer:0.065A$