Analysis of Rectangular Loop in Uniform Magnetic Field

In summary, we discussed the scenario of a rectangular loop being dropped into a uniform magnetic field with a mass of m and resistance of R. The loop has dimensions of length L, breadth b, and L tending to infinity. We also considered the presence of gravity in the downward direction and how it affects the loop. Through calculations, we determined that the emf induced is equal to Bvb and the current is Bvb/R. We also looked at the forces acting on the loop as it enters the field region and discussed how to deduce the direction of induced current using Lenz's law. We also addressed a clarification about the forces on each side of the infinite length and how the net force can be determined. Ultimately, we concluded
  • #1
Ganesh
13
0
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?
 
Last edited:
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  • #2
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.
 
  • #3
Oh you seem to have put some equations now...lemme see.
 
  • #4
I just edited myn post now
 
  • #5
maverick280857 said:
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.

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  • #6
I did just that.
 
  • #7
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
 
  • #8
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.
 
  • #9
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 [tex]\infty[/tex] 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.
 
Last edited:
  • #10
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)
 

1. What is a rectangular loop in a uniform magnetic field?

A rectangular loop is a closed circuit made up of four straight sides with equal lengths and four right angles. It is placed in a uniform magnetic field, which means that the magnetic field has the same strength and direction at all points within the loop.

2. How does a rectangular loop behave in a uniform magnetic field?

When a rectangular loop is placed in a uniform magnetic field, it experiences a torque or turning force. This torque causes the loop to align itself with the direction of the magnetic field. The loop will continue to rotate until it is perpendicular to the magnetic field lines.

3. What is the purpose of analyzing a rectangular loop in a uniform magnetic field?

The analysis of a rectangular loop in a uniform magnetic field allows us to understand the behavior and properties of magnetic fields. It also has practical applications, such as in the design of electric motors and generators.

4. How is the torque on a rectangular loop calculated?

The torque on a rectangular loop in a uniform magnetic field can be calculated using the equation: T = NIA x B, where N is the number of turns in the loop, I is the current flowing through the loop, A is the area of the loop, and B is the strength of the magnetic field.

5. What factors affect the torque on a rectangular loop in a uniform magnetic field?

The torque on a rectangular loop is affected by the strength and direction of the magnetic field, the current flowing through the loop, and the size and orientation of the loop. Additionally, the number of turns in the loop and the material of the loop can also impact the torque.

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