Find I(coil): Solenoid & Coil Setup

[splac6996]

Homework Statement

A 44.0 -turn, 3.90-cm-diameter coil with R(resistance) = 0.510 surrounds a 2.40-cm-diameter solenoid. The solenoid is 16.0 long and has 240 turns. The 60 Hz current through the solenoid is I(solenoid)= 0.530Asin2$$\pi$$ft.

Homework Equations

Find the value of I(coil), the induced current in the coil at time = 1.22 .

The Attempt at a Solution

I am not sure if I am on the right track, I found an expression for the flux through the coils and then found the induced emf. Is this the correct way to go about it.

 

[foxjwill]

Yes, it is.

 

[Moetasim]

Yes, you are on the right track. To find the induced current in the coil, you can use Faraday's law of induction which states that the induced emf is equal to the rate of change of magnetic flux through the coil. In this case, the magnetic flux through the coil is changing due to the changing current in the solenoid. By using the given values for the solenoid current and the number of turns in the coil, you can calculate the change in magnetic flux. Then, using Ohm's law (V=IR), you can find the induced current in the coil. Make sure to consider the direction of the current and the polarity of the induced emf.