Magnetic Field and Induced Currents in Rails Problem

[phyphysics]

Consider the following problem:

There is a uniform magnetic field pointing into the page. A set of rails is placed horizontally inside the field. A metal rod can slide freely on the rails, when we apply a force to move the rod to the right, is there any induced current in the rod when moving it inside the uniform field?

 

[KingOfTwilight]

Yes there is current if the circuit is closed.
$$E = bvB \sin{\alpha}$$, here $$\alpha = \pi$$.
You can deduce the latter from this: $$E = \frac{d \Phi}{dt}$$ when you remember that $$A (t) = ab (t) = vtb$$.

 

[marlon]

Consider the following problem:

There is a uniform magnetic field pointing into the page. A set of rails is placed horizontally inside the field. A metal rod can slide freely on the rails, when we apply a force to move the rod to the right, is there any induced current in the rod when moving it inside the uniform field?

yes there will be an induced current. The direction of that current will be so that the resulting Lorentz force on the rod will counter the force you exterted when pushing the rod to the right.

marlon

 

[phyphysics]

But isn't that the wire does not encounter any change in magnetic flux? How can current be induced if the magnetic flux does not change?

 

[eep]

why do you think the flux isn't changing? what's the effect of sliding the metal bar to the right?

 

[marlon]

But isn't that the wire does not encounter any change in magnetic flux? How can current be induced if the magnetic flux does not change?

in order to change the flux you can alter two variables:
1) the magnitude of the B field, but this is constant here
2) the surface through which the B lines pass, this changes because of the rod-displacement

marlon

 

[phyphysics]

But how can current be induced when it moves along the UNIFORM magnetic field?

 

[marlon]

But how can current be induced when it moves along the UNIFORM magnetic field?

because the flux changes

or

because you have a moving wire in a magnetic field. Don't you know what Maxwell says about this ?

marlon

 

[phyphysics]

So what exactly are the conditions for current to be induced?

 

[marlon]

So what exactly are the conditions for current to be induced?

Well, a changing flux induces an EMF and thus a current, that is all.
If the flux rises, then the induced current will have such a direction that the associated induced B field will counter act to the rising flux. this is just Lenz's law in a more general form

Also, according to the Lorentz-force formula, you know that if a wire moves in a magnetic field, a current must flow through that wire

marlon

 

[mukundpa]

Simply, if the circuit is closed it means some other connection between the two rails. Then this connection with rails and the rod encloses some area and this area is changing due to movement of the rod, hence the flux through this area is changing, inducing current.