Question

The diagram shows two loops of wire. The outerloop is a circuit with a switch, a battery, a capacitor (which starts out uncharged), and a resistor. The inner loop is just a wire. The two loops are not connected to each other electrically.

https://scontent-iad3-1.xx.fbcdn.net/v/t1.15752-9/31963888_10211369349701547_3712409743130624000_n.jpg?_nc_cat=0&oh=10908d4f57a4ae22b17f20aefe6b43d9&oe=5B51BF2B

a. At time 0, the switch is closed. At some later time t1, what is the firection of the current in the outer loop? How do you know?

b. From time t1, to a later time t2, is the current in the outer loop changing? Explain how and why.

c. What is the direction of the magnetic field inside the inner loop? Explain.

d. Is there an induced current in the inner loop? If so, what is the direction of the current? Explain

Answer 1

a)

In the outer circuit, as the capacitor gets charged, the magnitude of current in clockwise direction decreases. hence the magnetic flux through the inner loop inward direction decreases. the inner loop oppose this change by inducing current in itself so as to increase magnetic field in inward direction, To have the magnetic field in inward direction, the inner loop must have current in clockwise direction as per right hand rule.

b)

yes the current is changing.

this is because as the capacitor gets charged more and more with time, the current in the circuit decreases

c)

since the current in outer loop is in clockwise direction , using right hand curl rule , direction of magnetic field inside the inner loop comes out to be in inward direction

d)

yes there is induced current in inner loop as the magnetic flux in inward direction linked with the inner loop is decreasing. To oppose the change , the inner loop induce current in itself to produce magnetic field in inward direction to compensate for the decrease in magnetic field in inward direction

hence the current induced is in clockwise direction as per right hand rule