A long straight wire is parallel to one edge and is in the plane of a single-turn rectangular loop as shown. If the loop is moving in the plane shown so that the distance x changes at a constant rate of 20 cm/s, what is the magnitude of the emf induced in the loop at the instant x = 5.0 cm? Let / = 50 A, a = 50 cm, b = 6.0 cm.

The magnitude of the emf induced in the loop is 2.4 × 10⁻⁵ V

Explanation:

The magnitude of the induced emf of a loop moving relative to a wire is given as follows;

The given parameters are;

I = 50 A, a = 50 cm, and b = 6.0 cm

The constant rate of change of x, v = 20 cm/s

Motional emf formula

The magnetic field due to the straight wire, B = μ₀·i/(2·π·x)

The flux given by the rectangular loop, Ф = BA =  μ₀·i/(2·π·x) × a × b

Therefore, we get;

Therefore;

μ₀ = 4·π × 10⁻⁷ H/m

We get;

The induced emf, e = 2.4 × 10⁻⁵ V