Question

A long straight wire has a current that is decreasing at a rate of 23 A/s and is directed as shown on the attached figure. There is a single rectangular loop of wire near the long wire located as shown on the figure.

a) Determine the induced EMF in the loop.

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

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Answer 1

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.