# Electromagnetic induction - which graph is correct?

1. Nov 13, 2009

### joeykeys

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

A 10 cm by 10 cm square coil with 3 turns moves into a magnetic field 30 cm wide and of strength 10.0 T to the right of the diagram at a speed of 0.10 m/s as shown.

http://two.xthost.info/joeykeys/1.png

Sketch a graph of the induced voltage versus time, starting time when the front edge of the coil is 0.20 m outside the field, and ending when the last side of the coil is 0.20 m outside the field. Show values at the important points on the graph.

3. The attempt at a solution

Solution A:
http://two.xthost.info/joeykeys/2.png

Solution B:
http://two.xthost.info/joeykeys/3.png

I would like to know whether attempt A or attempt B is correct?..
or..if there is another solution?

Thank you so much for your time!
Graphs are sketched in Word, so, they are not to scale at all :)

2. Nov 13, 2009

### Andrew Mason

What is the condition for 0 induced emf? When does that condition start to apply? When does it end?

AM

3. Nov 14, 2009

### joeykeys

Looks like A to me...

Thinking process:
he separation between the induced e.m.f. is 3 seconds. So it is A.

Why 3 seconds?
Consider Alice on the left edge and Bob on the right edge of the B-field grid with the synchronized clocks.

The induced emf exists only if there is a cut by the edges (a non-empty changing area of intersection between the coil and the field).

Setup:
Alice starts recodring the time when the cut starts and finishes on the left edge, while Bob does the same when the same happens on the right.

Running:
When the right edge of the coil just cuts the left edge of the B-field grid, we know the induced voltage starts to be non-zero. According to Alic, it is the 2nd second.

But the coil with length 0.1m moves at speed 0.1m/s. So just after one second, the changing area of intersection is zero. Hence no induced emf. The cut finishes on the left at the 3rd second according to Alice.

At this time the coil still has 0.2 m separation to completely escape the B-field grid. It obviously tells u the following...

At the 5th second, Bob sees the coil is just well inside the field with zero interchaning area of intersection.

So according to our physical principle, induced emf is zero from the 3rd to 5th second. In fact, this immediately yields A.

Does it make sense?...:)

4. Nov 14, 2009

### Andrew Mason

Yes. A is correct. Your reasoning could be clearer:

1. The condition for 0 emf is that the rate of change of flux through the coil is 0:

$$\varepsilon = \dfrac{d\phi}{dt} = 0$$ (Faraday's law).

2. The time rate of change of flux enclosed by the coil is zero only when the coil is entirely within the 30 cm rectangular B field or entirely outside it. This occurs before any of the right side of the coil has entered the field; after the right side of the coil has moved 10 cm into the field and until it reaches the right edge of the field; and after the left edge leaves the field.

AM