# Induced EMF in Non-Uniform Magnetic Field

1. Jul 8, 2011

### arl146

1. The problem statement, all variables and given/known data
A square wire loop of dimensions L X L (L = 15.5 cm) oriented in the xy-plane and centered on the x-axis enters a region where the magnetic field (B = 0.855 T) is first oriented in the +z- and then in the -z-direction as shown in the diagram below. (Note: W = 15.501 cm and the magnetic field is zero outside the shaded area.) The loop moves at speed v = 4.55 ms in the +x-direction. In the questions that follow, when asked for the emf, a positive emf will be defined as an emf induced counterclockwise (if viewed from above the loop); and vice versa.

(i.) What is the induced emf in the loop when the center of the loop is at x = -W?
(ii.) What is the induced emf in the loop when the center of the loop is at the origin?
(iii.) What is the induced emf in the loop when the center of the loop is at x = +W/2?
(iv.) What is the induced emf in the loop when the center of the loop is at x = +W?

2. Relevant equations
See below

3. The attempt at a solution
I think if I get help on one of them, then I should be able to figure out the others.
I'm not too sure how to approach this one, but I was thinking to use E=Blv or the flux=BA equation. But I'm not sure how that works out

2. Jul 11, 2011

### arl146

no one can help me with this ? =/

3. Jul 14, 2011

### arl146

still looking for help ...

4. Jul 14, 2011

### WatermelonPig

In general emf = vBL for these sorts of situations but a drawing would be nice.

5. Jul 14, 2011

### cupid.callin

As WatermelonPig said, EMF=vBl
and its polatiry can be found out by F=q vXB (cross product)

bt we need a diagram to understand the question

6. Jul 15, 2011

### arl146

Oh, sorry, wasnt paying attention that I didn't have one attached!

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7. Jul 15, 2011

### cupid.callin

(i) when center will be at x=-w ... which part of loop will be inside mag. field area and which part will induce emf (for this, you should have studied motional emf)

8. Jul 15, 2011

### arl146

only half of the loop will be inside the magnetic field that is pointing up. the left side half isn't in a B field. So just the right side that's in the magnetic field induces emf?

9. Jul 15, 2011

### cupid.callin

yes, thats correct :)

10. Jul 15, 2011

### arl146

so, what does that mean haha i still am not sure what to do for it

11. Jul 15, 2011

### cupid.callin

you did first
now for second, you need to find polarity of induced emf in on the 2 wires (left and right) of loop ...

for this use the formula of force on moving charge in mag. field, $\vec{F} \ = \ q \ \vec{v} \times \vec{B}$

As you would know, the wire moving in mag. field will act like a battery with a (+) and a (-) pole.
suppose there is a positive charge in wire moving with wire ... find direction force on it (generally along wire in these kind of questions). the side where + charge moves is (+) and other is (-)

thus find net emf in wire in case (ii)

12. Jul 16, 2011

### arl146

so wait .. i dont get it, how did i do the first one?

and for (ii.) how do you use that without q ?

Last edited: Jul 16, 2011
13. Jul 16, 2011

### vela

Staff Emeritus
Since you're dealing with a loop, it would be more straightforward to calculate the rate of change of the magnetic flux through the loop to find the emf.

14. Jul 17, 2011

### cupid.callin

motional EMF in a wire moving in mag field is vBL , here v is velocity B is mag field and L is the length.

15. Jul 17, 2011

### arl146

i did that already it was wrong

16. Jul 17, 2011

### cupid.callin

is it sign problem or magnitude is wrong?

17. Jul 17, 2011

### arl146

Oh wait, I got it now :)
Okay, for the second: i dont get what youre saying for that ..

18. Jul 25, 2011

### arl146

Can I please have some help on the other one's then?

19. Jul 25, 2011

### cupid.callin

do you know how to find polarity of the charges in a wire?

20. Jul 25, 2011

### arl146

i dont think ... im not too sure what that means