EMF induced in a wire loop rotating in a magnetic field

  • #1
LCSphysicist
634
153
Homework Statement:
.
Relevant Equations:
.
1655168640334.png


To solve this problem, we need to evaluate the following integral: $$\epsilon = \int_{P}^{C} (\vec v \times \vec B) \vec dl$$

The main problem is, in fact, how do we arrive at it! I can't see why a Electric field arises at the configuration here. The magnetic field of the rotating sphere is time independent ##(\frac{ d \omega }{dt}) = 0##. The magnetic dipole at the center is also time independent.

So why do a electric field arise? Worst: Why do it arise and is equal to ##\vec v \times \vec B##?
 

Answers and Replies

  • #3
LCSphysicist
634
153
Have you studied motional emf?
It is more about the difficult to see that the area to calculate the flux is constant in avarage, but in infinitesimally time it is varying?
 
  • #4
TSny
Homework Helper
Gold Member
13,837
4,013
So why do a electric field arise? Worst: Why do it arise and is equal to ##\vec v \times \vec B##?
This link might be helpful.
 
  • #5
Delta2
Homework Helper
Insights Author
Gold Member
5,695
2,473
The Lorenz force ##F_L=(v\times B)q## makes the electrons move, and this creates charge separation or simply charge density ##\rho\neq 0##. This charge density creates electric field according to Gauss's law $$\nabla\cdot \mathbf{E}=\rho$$.
How do we know that the line integral of this electric field equals to $$\int_C^P \mathbf{E}\cdot d\mathbf{l}=\int_C^P(\mathbf{v}\times\mathbf{B})\cdot d\mathbf{l}$$.

Well we also impose the additional equilibrium condition $$F_E=F_B\Rightarrow \mathbf{E}q=-(\mathbf{v}\times\mathbf{B})q$$

I am feeling we 'll have to open some can of worms if we going to discuss why this equilibrium condition holds but anyway that is my take on this problem.

P.S In my opinion the equilibrium condition holds approximately in the quasi static approximation, that is when B and v are independent of time or vary slowly in time so that the charges move to the equilibrium position almost instantaneously.
 
Last edited:

Suggested for: EMF induced in a wire loop rotating in a magnetic field

Replies
18
Views
603
Replies
8
Views
435
Replies
21
Views
507
Replies
12
Views
477
Replies
3
Views
413
Replies
5
Views
482
Replies
41
Views
1K
Replies
4
Views
193
Replies
15
Views
583
Top