Force between two perpendicular wires

[Eitan Levy]

Homework Statement

In a system as described in the picture, what would be the force that the infinite wire with a current of i exerts on the wire BC?

Relevant Equations

F=BILsinΘ

μThe magnetic field is supposed to be B=μ₀i/(2πr). I think that the force would be aimed upwards.

Now I tried to divide the wire BC to infinite smaller wires where B is roughly constant in each one of them.

What I get is:

However this is not correct when I plug the relevant numbers in it.

Where is my mistake?

 

[TSny]

Your work looks basically correct.

I think there's a sign error on the right-hand side. Is the force $\vec{dF}$ in the same direction as $\vec B \times \vec{dl}$? I assume that you are using the usual convention that $\vec{dl}$ is in the same direcrion as the current in $dl$.

The left side is a vector quantity while the right side is a scalar quantity. So, you should include a unit vector on the right side to indicate the direction of the quantity on the left side.

Your final result looks correct for the magnitude of the force on BC. Were you also expected to give the direction of the force?

 

[kuruman]

How do you know that you plugged in the numbers correctly? Show us the numbers and exactly what you did. Also, the force is $d\vec F=Id\vec l \times \vec B$. You show the negative of this.

 

[Eitan Levy]

I indeed plugged the numbers wrong. Thanks for the heads up about the wrong direction of dF, I will be more careful.