Analysis of Rectangular Loop in Uniform Magnetic Field

[Ganesh]

What happens when a rectangular loop is dropped into a field of uniform, magnetic field B extending to infinity?
The loop has a mass m and its resistance is R.
It has length L, breadth b, L tending to infinity.
Gravity is present in downward direction.
The loop is dropped such that emf is induced across one breadth.


Emf induced = Bvb
Current = Bvb/R.
Force net = mg - Bvb*b*B/R
accn = dv/dt = g - B^2vb^2/mR
Integrating an expression in log is obtained which does not match the reqd answer given in a book.

Is the method correct?

 

[maverick280857]

What are the forces on the loop as it enters the field region? How can you deduce the direction of induced current in the loop as the flux linking it changes dynamically? Hint: use Lenz's law.

 

[maverick280857]

Oh you seem to have put some equations now...lemme see.

 

[Ganesh]

I just edited myn post now

 

[Ganesh]

What are the forces on the loop as it enters the field region? How can you deduce the direction of induced current in the loop as the flux linking it changes dynamically? Hint: use Lenz's law.

aaaaaaaaaaaaaaaa

 

[Ganesh]

I did just that.

 

[maverick280857]

The loop consists of 4 segments: 2 of length L and 2 of length b. Each segment carries the same current.

Note: I do not understand so many a's in your last post. Please do not waste our time and resources (no offence meant). I obviously made that post before you put up the equations (before which you seemed to be unable to start correctly...now you're finishing incorrectly!).

Cheers
Vivek

 

[Ganesh]

Since l is infinite, the second side of bredth b never enters the field.
Also, the force on each of the sides of infinite length is equal and opposite.
So net force is the expression I typed out.

 

[maverick280857]

Look if you're going to keep changing your original post, we'll have no reference to see and its pointless helping you!

Remember to post your complete reasoning and solution on PF before asking for help.

Cheers
Vivek

EDIT: If L (and not l) tends to \infty then as you have correctly reasoned, it shouldn't directly appear in the expressions though I would've preferred to use some finite L and eventually let it go to infinity if possible. Of course that isn't the question we're doing now.

Appears fine (except the first form)...will post in detail later.

 

[Ganesh]

I have written all the equations I know.
Is the application correct?

P.S. I did not know you had typed out replies before I had finished editing (which I did immediately after my post came up)