# Homework Help: Two movable wires in Magnetic Field

1. May 4, 2016

### Vibhor

1. The problem statement, all variables and given/known data

2. Relevant equations

EMF induced in a moving wire =Bvl

3. The attempt at a solution

When right wire is given a velocity v , an initial emf Bvl is induced in right wire due to which current starts flowing in the loop .

Initial current i = Bvl/(2R)

The left wire experiences a repulsive force due to right wire towards left .It also experiences a force of magnitude ilB towards right due to the magnetic field .

Similarly , the right wire experiences a repulsive force due to left wire towards right .The speed of left wire changes which means the emf induced varies .As a result the current flowing is not constant .

I am unable to proceed .

Thanks

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Last edited: May 4, 2016
2. May 4, 2016

### TSny

I suspect that you are meant to neglect the force of one wire on the other wire compared to the force that each wire experiences from the external B field.

3. May 4, 2016

### cnh1995

I believe forces on wires due to each other should also be neglected since distance between them is not mentioned here.

4. May 4, 2016

### Vibhor

Ok .

In that case force on left wire would be towards right and that on right wire would be towards left . The left will accelerate towards right and right would decelerate i.e v decreases. Right ?

5. May 4, 2016

### cnh1995

Yes. Right wire will stop eventually(momentarily) while left wire will have some velocity towards right. This problem is interesting!

6. May 4, 2016

7. May 4, 2016

### TSny

Will the right wire ever stop?

8. May 4, 2016

### Vibhor

Last edited: May 4, 2016
9. May 4, 2016

### cnh1995

I believe there will be a moment when emf induced in the right wire will be 0 and left wire will have a velocity(maximum) towards left. From that moment onwards, left wire will act as a generator and push the right wire again towards right.
Edit: No, I think it won't stop at all. When velocity of the left wire will become greater than that of the right wire, it will push the right wire again towards right.

10. May 4, 2016

### Vibhor

Momentum conservation ?

mv = 2mv' i.e final speed =v/2 .

Both the sliders would move together towards right with speed v/2 after long time .

Is that what you are hinting at ??

Last edited: May 4, 2016
11. May 4, 2016

### TSny

It's your problem . Give me a reason why the momentum should be conserved.

12. May 4, 2016

### Vibhor

Because no net horizontal force on the system of two rails . The force due to magnetic field is always equal in magnitude and opposite in direction .

So , mv = 2mv' i.e final speed =v/2 .

Both the sliders would move together towards right with speed v/2 after long time .

13. May 4, 2016

### TSny

Are you saying that the net force on the system consisting of the two wires is zero? Why?

Why are the final speeds of the two wires equal to each other?

14. May 4, 2016

### TSny

Will the speed of the left wire ever become greater than the speed of the right wire?

15. May 4, 2016

### Vibhor

Force ilB acts leftwards on right wire and force ilB acts rightwards on left wire . On the whole ,they cancel each other ??

The left wire accelerates towards right and right accelerates towards left till they meet . Afterwards they move together (presuming momentum conservation )

I am bereft of ideas

16. May 4, 2016

### TSny

OK. At any instant of time the two wires (sliders) have the same magnitude of current and the currents are opposite in direction. So, the net force on the system of the two sliders is zero. So, linear momentum is indeed conserved! Good.
Until they meet? You mean the two wires are going to collide? If so, you would need to know some information about the collision (elastic or inelastic, etc.) I think you can assume that the wires never touch each other. [EDIT: There's a good argument for why they never meet. See my question in post #14.]
What happens to the magnitude of the induced emf as time increases? Why?

Last edited: May 4, 2016
17. May 4, 2016

### Vibhor

I think there will also be an induced emf in the left wire as it starts to move. Polarity of emf in left wire will be opposite to that of right wire . Do I need to consider this ?

18. May 4, 2016

### Vibhor

Why not ? left wire accelerates rightwards wheras right wire decelerates .What stops left wire from gaining higher speed than right one .

19. May 4, 2016

### TSny

Consider the total instantaneous emf induced in the circuit that consists of the two slider and the rails. What law is relevant?

20. May 4, 2016

### TSny

First investigate how the instantaneous current in the circuit depends on the instantaneous velocities of the sliders.

21. May 4, 2016

### Vibhor

$i=\frac{Blv}{2R}$ ??

22. May 4, 2016

### Vibhor

23. May 4, 2016

### TSny

No, the current in the circuit is determined by the total emf induced in the circuit.

24. May 4, 2016

### TSny

Yes. Or, equivalently, you can get an expression for the total emf by combining the motional emfs of the two sliders

25. May 4, 2016

### Vibhor

$i = \frac{Bl}{2R}(v_2-v_1)$