A 4 cm x 10 cm rectangular loop of wire with a net resistance of 4 ? is oriented

Question

A 4 cm x 10 cm rectangular loop of wire with a net resistance of 4 ? is oriented perpendicular to the z axis. Before time t = 0, a 5 T uniform magnetic field exists in the +z direction (into the page) as shown in the figure. For all other times, the strength of the field is given by the curve to the right.

1)

Which way is the current flowing in the wire loop at time t = 2 s?

2)

What is the value of the magnetic flux through the loop at time t = 0.5 s?

3)

Which way is the current flowing in the wire loop at time t = 3 s?

4)

Calculate the magnitude of the current at t = 4.5 s.

Explanation / Answer

Here ,

1) at time t = 2 s

as the magnetic field is decreaseing . current will flow such that the induced magnetic field is in the direction of initial magnetic field

the curernt is clockwise

2)

at t = 0.5 s

magnetic flux = 0.04 * 0.10 * 5

magnetic flux = 0.02 T.m^2

3)

at t = 3

as the magnetic field has started increasing ,

the induced magnetic field will oppose the change

and the current is flowing in anti clockwise direction

4)

at t = 4.5 s

induced current = 0.04 * 0.10 * (10 - (-5))/(2 * 5)

induced current = 0.006 A

the induced current at t = 4.5 s is 0.006 A

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