# Induced EMF in a moving conductor #### Everything You Need in One Place

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##### Intros
###### Lessons
1. Introduction to induced EMF in a moving conductor.
2. Magnitude of the electromotive force.
3. Direction of the induced current and electromotive force.
##### Examples
###### Lessons
1. A 1.2m length of wire is pulled through a uniform 0.045 T magnetic field at 6.7m/s as shown. What emf is generated between the ends of the wire? 1. 0V
2. 0.090V
3. 0.36V
4. 0.45V
2. A solid conductor travels at 150m/s across a uniform 0.045T magnetic field. Which side is positively charged and what is the emf across this block? 1. The circular loop of wire shown below has an area of 0.40 $m^{2}$ and is in a 0.60T magnetic field. This filed increased to 1.40 T in 0.25 $s$. 1. A 0.050m long conducting wire is moved through a 1.5 T magnetic field as shown below. What is the magnitude of the emf generated between its ends, and in what direction do the electrons in the conductor initially move? 1. A circular loop of resistance 1.2 $\Omega$ is pulled a distance of 0.40m into a perpendicular magnetic field as shown below. an average current of 0.50A is produced in the coil during this event. Calculate the constant speed with which the coil was pulled.
1. 0.10 m/s
2. 0.75 m/s
3. 1.9 m/s
4. 2.4 m/s
2. A 0.75 m conducting rod is moved at 8.0m/s across a 0.25 T magnetic field along rails. The electrical resistance of the system is 5.0 $\Omega$. What are the magnitude and direction through point $X$?  1. A 200-turn coil has a 15.2 V potential difference induced in it when the magnetic field changes from 0.42 T to 0.22 T in the opposite direction in 3.2 ×10?2 $s$. What is the radius of this coil? 1. 3.5 × 10?2m
2. 5.1 × 10?2m
3. 5.9 × 10?2m
4. 6.2 × 10?2m
###### Topic 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

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

$l$ = 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.

• 