Induced EMF in a moving conductor - Electromagnetic Induction

Notes:

In this lesson, we will learn:

• Moving a conductor in a uniform magnetic field results in an induced emf across the conductor.
• How to find the magnitude of the electromotive force?
• How to find the direction of the electromotive force?

Notes:

• Moving a conductor in a uniform magnetic field results in an induced emf across the conductor.
• As the conductor moves, there is a change in magnetic flux, due to the change in area of the conductor that is exposed to the magnetic field lines.




• Change in flux results in electromotive force induction and induced emf in the loop.


Magnitude of the Electromotive Force


• According to Faraday’s law:

$\large \epsilon = \frac{\Delta \phi} {\Delta t}$

$l$ = length of the rod
$B$ = magnetic field
$v$ = speed of the rod
$A$ = area of the loop

If the rod moves at speed of $v$, it travels a distance of $\Delta x$, in a time $\Delta t$;

$\Delta x = v \Delta t$
Therefore, the area of the loop changes by an amount of $\Delta A$ = $l \Delta x$

$\large \epsilon = \frac{\phi} {\Delta t} = \frac{B \Delta A} {\Delta t} = \frac{Blv \, \Delta t} {\Delta t} = Blv$


Direction of the Induced Current and Electromotive Force

• The direction of the induced current is in a way to oppose the change in flux.