What is electromagnetic induction? State the laws of electromagnetic induction - Leaving Cert Physics - Question 8 - 2008

1. Faraday's Law: The induced emf in a closed loop is directly proportional to the rate of change of magnetic flux through the loop. It can be expressed mathematically as:

   $E = -N \frac{d\Phi}{dt}$

   where $E$ is the induced emf, $N$ is the number of turns in the coil, and $\Phi$ is the magnetic flux.

2. Lenz's Law: The direction of the induced current and emf will be such that it opposes the change in magnetic flux that produced it.

As the bar magnet swings, it moves through the copper sheet, generating an induced emf due to the change in magnetic flux. The induced current flows through the copper sheet, creating its own magnetic field that opposes the motion of the magnet, as described by Lenz's Law. This interaction converts some of the mechanical energy of the swinging motion into electrical energy, resulting in the rapid decrease in swing amplitude.

The main energy conversion occurs between kinetic energy and electrical energy. As the magnet slows down, some of its kinetic energy is converted into electrical energy due to the induced current in the copper sheet.

To determine how long it takes for the loop to completely enter the field, we use the formula:

$t = \frac{d}{v}$

where $d$ is the side length of the square loop (5 cm = 0.05 m) and $v$ is the velocity (5 m/s):

$t = \frac{0.05 \, \text{m}}{5 \, \text{m/s}} = 0.01 \, \text{s}$

The magnetic flux ($\Phi$) through the loop can be calculated using the formula:

$\Phi = B \times A$

where $B$ is the magnetic flux density (8 T) and $A$ is the area of the loop (for a square with side length 0.05 m):

$A = (0.05 \, \text{m})^2 = 0.0025 \, \text{m}^2$ Thus: $\Phi = 8 \, \text{T} \times 0.0025 \, \text{m}^2 = 0.02 \, \text{Wb}$

The average induced emf ($\text{emf}$) can be calculated using:

$\text{emf} = \frac{\Delta \Phi}{\Delta t}$

where $\Delta \Phi$ is the change in magnetic flux (0.02 Wb) and $\Delta t$ is the time taken to enter the field (0.01 s):

$\text{emf} = \frac{0.02 \, \text{Wb}}{0.01 \, \text{s}} = 2 \, \text{V}$