This is a homework question that I have stuck for a while and couldn't able to come up with the correct answer.

So here is the question, My thoughts towards this question

• When I move the rod PQ with a constant velocity ,the area of triangle RPQ inside the magnetic field increases .
• Once the area inside the magnetic field increases E.M.F induces also increases.
• Since induce E.M.F get increased the induced current should also be increased.

So according to my arguments I choose the answer as the third one. But the answer in marking scheme is the first one.

What I have done wrong. Please explain this question with details.

The question asks for the current, not the voltage.

The voltage (emf) generated would follow a straight line (not a curve) as the rate at which the area grows is proportional to the length of the wire - and the length of the wire grows linearly.

The current that flows as a result of this depends on the resistance of the loop. The circumference of the loop grows linearly with the horizontal position of the wire (similar triangles - when the wire has moved twice as far to the right, all the sides are twice as big).

The current is voltage divided by resistance. Both grow linearly; their ratio is constant.

• Please floris explain little bit more , specially the theory parts I want to use . A kind request Jun 30, 2015 at 14:47
• your first two bullet points are exactly right, but then you need Ohm's Law: I = V / R. And R scales with the length of the wire, just like V did. There is really nothing more to say. Jun 30, 2015 at 14:49
• I think ,we need to move this to a chat, isn't it? Jun 30, 2015 at 14:50
• Because I have confused with some facts Jun 30, 2015 at 14:50
• Or please explain this with more , like you did in previous questions.You helped me lot Mr.floris Jun 30, 2015 at 14:55

The voltage (or EMF) between P & Q is a constant given constant length, velocity and magnetic field, lets call it V.

The voltage between R & S is RS/PQ V, the induced current is through RBQ is equal to RS/PQ V/R by Ohms law.

Let L be the distance to the right of B that the wire is.

RS=2Ltan30

Assuming constant resistivity in the wire (r),

R=4Lrtan30

So, I = 2Ltan30/PQ V / 4Lrtan30 = V/2PQr

Which is independent of L

• Could you explain this little bit more ? Jun 30, 2015 at 10:43