An elastic circular conducting loop expands at a constant rate in time. The radius is initially 0.200 m. but then begins to increase 0.018 m every second. The loop has a constant resistance of 15 Ohm and Is placed in a region of uniform (same everywhere) magnetic field of 0.880 T, perpendicular to the plane of the loop. Calculate the magnitude of the Induced curt 2.4 s after the loop begins expanding.

4.5 mA

Explanation:

Parameters given:

Initial radius of coil = 0.2 m

Rate of expansion of coil = 0.018 m/s

Resistance, R = 15 ohms

Magnetic field, B = 0.88 T

Time taken to expand, t = 2.4 s

To find the induced current, we have to first find the induced EMF. This can be gotten by using the formula below:

where A = area of coil

To find the area, we need to find the radius of the coil 2.4 seconds after it started expanding.

After 2.4s, the coil had expanded to become:

r = 0.2 + (0.018 * 2.4) = 0.2 + 0.0432 = 0.2432 m

Area = =

The magnitude of the Voltage induced will be:

From Ohm's law, we have that:

=>

The magnitude of the Induced curt 2.4 s after the loop begins expanding is 4.5 mA