Question 254: Electromagnetic Induction

Question

A square loop ABCD is moving with constant velocity ' $\vec{v}$ ' in a uniform magnetic field ' $\vec{B}$ ' which is perpendicular to the plane of paper and directed outward. The resistance of coil is ' $R$ ', then the rate of production of heat energy in the loop is [ L - length of side of loop]

Accepted Answer

The rate of production of heat energy in the square loop due to its motion in a magnetic field can be determined using Faraday's Law of Electromagnetic Induction and Ohm's Law.
Induced EMF ($\mathcal{E}$):
The induced EMF in the loop moving with velocity $\vec{v}$ in a uniform magnetic field $\vec{B}$ is given by:
$$ \mathcal{E} = B \cdot L \cdot v $$
where:
$B$ is the magnetic flux density,
$L$ is the side length of the square loop,
$v$ is the velocity of the loop perpendicular to $B$.
Current ($I$):
The current induced in the loop, by Ohm's Law, is:
$$ I = \frac{\mathcal{E}}{R} = \frac{B \cdot L \cdot v}{R} $$
Power (Rate of Production of Heat Energy):
The power converted into heat (rate of production of heat energy) due to the induced current is given by:
$$ P = I^2 \cdot R $$
Substituting the expression for $I$, we get:
$$ P = \left(\frac{B \cdot L \cdot v}{R}\right)^2 \cdot R = \frac{B^2 \cdot L^2 \cdot v^2}{R} $$
Thus, the rate of production of heat energy in the loop is:
$$ \frac{B^2 L^2 v^2}{R} $$
Therefore, the correct answer is
Option B
:
$$ \frac{B^2 L^2 V^2}{R} $$

Answer

$\frac{B^2 L^2 V}{R}$

Answer

$\frac{B^2 L^2 V^2}{R}$

Answer

$\frac{B^2 L V^2}{R}$

Answer

$\frac{\mathrm{BLV}^2}{\mathrm{R}}$

Electromagnetic Induction

A square loop ABCD is moving with constant velocity ' \vec{v} ' in a uniform magnetic field ' \vec{B} ' which is perpendicular to the plane of paper and directed outward. The resistance of coil is ' R ', then the rate of production of heat energy in the loop is [ L - length of side of loop]

Choose the correct answer: