A long straight wire has a current that is decreasing at a rate of 23 A/s...

a)

The loop is rectangle therefore,

Area of loop = 10 * 2 = 20 cm²

Now,

Flux through coil is,

dΦ = di / dt = 23 A/s ……………… Equation 1

But definition of magnetic flux is,

Φ = B. A

Where, B = magnetic field and A = area of the loop

So,

B = Φ / A = (23 A/s) / (20 * 10^-4) = 115 * 10² tesla

The induced emf is,

ε= -N(d Φ / dt)

But N = 1 (No. of turns in the loop)

From equation 1

ε= - 23 v

b) The magnitude and direction of the induced current if the loop wire is made of aluminum and has a radius of 0.5 cm.

Area of the loop is,

A = π r² = 3.14 * (0.5 *10^-2)² = 0.785 *10^-4 m²

According to Lenz law,

The direction of current is clockwise if pole of the magnets are reversed from south to north. i.e. Initially, North pole is towards the loop.