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## Physics library

### Course: Physics library>Unit 13

Lesson 4: Magnetic flux and Faraday's law

# Emf induced in rod traveling through magnetic field

An emf induced by motion relative to a magnetic field is called a motional emf. This is represented by the equation emf = LvB, where L is length of the object moving at speed v relative to the strength of the magnetic field B.

## Want to join the conversation?

• If the area we were concerned with was the magenta area, then why wouldn't we want the magnetic field induced by the current to go down INSIDE the magenta area? Sal shows the current coming toward us because it would produce a field going down on the area to the left of the rod. This means the field is going UP inside the magenta area which adds to the existing flux. Isn't the magenta area the area of interest?? •  I think you are mistaken. The magenta area is only valuable for finding out the change in flux. When it comes to Lenz's law, we are concerned with the area to the left of the rod inside the loop. This is because the area on the right of the rod is not a loop, and thus, current cannot flow through it. Since the change in flux is increasing in the upwards direction, Lenz's law tells us that the induced current's induced magnetic field must resist that, and point downwards on the inside of the loop. Using the right hand rule, we can see that we end up with an induced current in the clockwise direction.
• After listening to this video, I got a little bit confused about the difference between the contents in this video and the Lorentz Force. Are these two processes exactly inverse? Please, who can help me! :) • The Lorentz Force is the force that makes the eletrons move, creating current on the wire. The force realizes work in the charges in the lenght L of the wire on the magnetic field, then if we divide the work by Q to get the work done per charge, we get J/C, which is the same as Volt. The Lorentz Force and the content in this video are two different ways to do the same thing. :)
• How does the coil moving slightly to the right increase magnetic Flux? It's just moving from one area to another, how is that 'increasing' area? • If two electric fields,for example,if 2 transformers are kept close,will there be a disturbance in the working of the transformers? • Shouldn't it be counter clock-wise? The purple arrows he drew seem to be going counter clock-wise. • Sal assumes a current direction when he first draws the purple arrow, but explains it violates Lenz's law. Later in the video, he switches the directions and explains how the clockwise direction is consistent with Lenz's law. According to Lenz's law, the induced current is always such that the induced magnetic field opposes the CHANGE in the existing magnetic field. In this case, the magnitude of the magnetic field is constant, but the flux increases because the area is increasing phi=BA
(1 vote)
• To be honest i have no question regarding your explanation. But i was wandering Sir, What if i want to derive an expression of motional induced E.M.F in a conducting rod rotated in magnetic field? I found it on internet an expression as E.M.F = 1/2*B*L^2W Where W (omega) = dA/dt where A = angle subtended in time t. That went pretty up above my head. • Hello Roushan,

It may help to simplify the model and talk about a machine that moves in a straight line:

Assumption #1: Let the velocity (v) be perpendicular to the magnetic field (B) where B is a vector

Assumption #2: Let the conductor be parallel with the vector v x B where B is a vector

Out model simplifies to e = Bvl

e is EMF
B is magnitude of the B field
v is velocity
l is length of the wire

Now to your question, ω can be substituted for the velocity term. Please give it a try. Place a point on the tip of the second hand of a clock. The angular frequency aka ω describes the velocity of this point.

Regards,

APD
(1 vote)
• So how do we determine the direction of the MAGNETIC FORCE acting on the bar? Is it opposite or same direction with the velocity of the bar?
(1 vote) • There's more than one way to do it, but the easy way is to use Lenz' law, which tells us that the induced EMF will oppose the change that is creating it. That means it has to, in this case, try to make the bar stop moving.

This makes sense because energy has to be conserved. If charge is moving, somehow energy is getting put into that system. Where does it come from? Whoever is pushing the rod. For that person to be doing work, they have to be exerting force in the direction that the rod is moving. But why should force be needed to keep the rod moving at constant velocity? It must be that there's an opposing force that the person doing the pushing has to fight against. If that person stops pushing, the opposing force will cause the rod to come to rest.

Think about what would happen if somehow the force was in the same direction as the velocity. You would give the rod a little push, and then that force would push it some more in the same direction, and then the rod would go faster so that force would get bigger, so the rod would go faster, etc etc etc. A tiny push would send the rod zooming off. Where would that energy come from to do that?   