Question

A single loop of wire with an area of 9.03×10-2 m^2 is in a uniform magnetic field that has an initial value of 3.66 T, is perpendicular to the plane of the loop, and is decreasing at a constant rate of 0.199 T/s.

What emf is induced in this loop?

If the loop has a resistance of 0.650 ohm, find the current induced in the loop.

Answer 1

Given that the area of loop is \(\mathrm{A}=9.03 \times 10^{-2} \mathrm{~m}^{2}\)

Magnitude of magnetic field is \(\mathrm{B}=3.66 \mathrm{~T}\) Rate of change of magnetic field is \(\mathrm{B} / \mathrm{T}=0.199 \mathrm{~T} / \mathrm{s}\)

From Faraday's law Induced emf in the loop is \(\varepsilon=-\frac{d \Phi}{d t}\)

$$ \begin{aligned} \varepsilon &=-\frac{d(B \cdot A)}{d t} \\ &=-A \frac{d B}{d t} \\ &=-\left(9.03 \times 10^{-2} \mathrm{~m}^{2}\right)(0.199 \mathrm{~T} / \mathrm{s}) \\ &=-1.79 \times 10^{-2} \mathrm{~V} \end{aligned} $$

The magnitude of induced emf in the coil is \(1.79 \times 10^{-2} \mathrm{~V}\) Then the induced current in the loop is

$$ \begin{aligned} \mathrm{I} &=\frac{\varepsilon}{R} \\ &=\frac{1.79 \times 10^{-2} \mathrm{~V}}{0.650 \Omega} \\ &=2.76 \mathrm{~A} \end{aligned} $$