What is the Force on a Rectangular Loop in a Magnetic Field?

[fogvajarash]

Homework Statement

Let d = 0.048m, L = 0.15m, r = 0.10m in the following diagram. Assume that the current I₁ = 80.0A and I₂ = 40.0A. Find the net force on the rectangle of wire and the direction it points, and state the direction of the emf if the current I¹ is increasing in the direction of the arrow.

Diagram: http://imgur.com/RmvkO9n

Homework Equations

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The Attempt at a Solution

I have that the force is given by F = BIl. In this case, B would come from the field created by the current I¹. So, we would get that the force will be (let force 1 be for the closest part of the loop and force 2 for the farthest part of the loop):

F₁ = \frac{μI₂I₁l}{2πd} ≈ -2x10^-3N
F₂ = \frac{μI₂I₁l}{2π(d+r)} ≈ 6.49x10^-4N

Then, the net force would be F_net = -1.35x10^-3N, pointing downwards. However, I get a mistake. Why is this the case? I'm thinking that my procedure is right until now, as there will be no force felt by the loop wires perpendicular to the long wire. I tried to perhaps calculate an induced current, but I can't do so as I don't have a resistance.

For the second part, the current would be induced to even out the flux change, so the induced B field should point down, leading to an opposite direction of the induced current as stated in the diagram. This is because the flux of the long wire would be increasing upwards in the plane of the wire.

 

[BvU]

Hi foggy, I can't see the diagram you are referring to !

 

[fogvajarash]

Hi foggy, I can't see the diagram you are referring to !

So sorry! I have uploaded it right now.

 

[BvU]

I would expect B to be smaller at r+d than at d, so |F| too. Wouldn't you ?

I suppose the ^-3 is really a ^-4 ?

How do you know you get a mistake ?

With $\mu = 4\pi 10^{-7}$ I get the same as you...

 

[fogvajarash]

I would expect B to be smaller at r+d than at d, so |F| too. Wouldn't you ?

I suppose the ^-3 is really a ^-4 ?

How do you know you get a mistake ?

With $\mu = 4\pi 10^{-7}$ I get the same as you...

My bad again sorry. The computer system is telling me that I have made a mistake (I'm not sure where though). In the meantime, is my reasoning for the flux current correct? Thanks for your time and patience.

 

[BvU]

Well, as I said, same result: same value, same direction.

Your reasoning for the induced emf is right, too. Since they don't tell us how the I₂ comes about, there isn't much more that can be said about the effects.

 

[fogvajarash]

Well, as I said, same result: same value, same direction.

Your reasoning for the induced emf is right, too. Since they don't tell us how the I₂ comes about, there isn't much more that can be said about the effects.

Thanks for everything thus far. Apparently there's been an error with the question grading, so I'm pretty sure our answer we have come up to is the correct one. Thanks for everything.