Question

3. A 500-loop circular wire coil with radius 4.00 cm is placed between the poles of a large
electromagnet. The magnetic field is uniform and makes an angle of 60° with the
plane of the coit: it decreases at 0.200 T/s. Magnitude of induced emf is
h 0.455 V
c 0.495 V​

Answer 1

Answer:

Faraday’s Law of Induction

Faraday’s law of induction states that the induced e.m.f. in a closed loop equals the negative of the time rate of change of magnetic flux through the loop.

$$\epsilon =- \frac{d\Phi_{B}}{dt}$$

Example: E.M.F. and current induced in a loop

The magnetic field between the poles of the electromagnet is uniform at any time, but its magnitude is increasing at the rate of 0.020 T/s. The area of the conducting loop in the field is $120 \, \text{cm}^{2}$, and the total circuit resistance, including the meter and the resistor, is $5.0 \, \Omega$. The induced e.m.f. and the induced current in the circuit is given by:

$$\begin{aligned} \epsilon &= \frac{dB}{dt}A \\ &= 0.24 \, \text{mV} \end{aligned}$$

$$\begin{aligned} I &= \frac{\epsilon}{R} \\ &= 0.048 \, \text{mA} \end{aligned}$$

If we have a coil with N identical turns, and if the flux varies at the same rate through each turn, the total rate of change through all the turns is N times a large as for a single turn. If $\Phi_{B}$ is the flux through each turn, the total e.m.f. in a coil with N turns is:

$$\epsilon =- N \frac{d\Phi_{B}}{dt}$$

Example: Magnitude & Direction Of An Induced E.M.F.