# Integrating over a cross product?

1. Nov 2, 2015

### Jonathan K

Lets look at the force on a wire segment in a uniform magnetic field

F = I∫(dl×B)

I am curious if, from this, we can say:

F = I [ (∫dl) × B] since B is constant in magnitude and direction

2. Nov 2, 2015

Yes, we can.

3. Nov 2, 2015

### Jonathan K

can you offer a proof?

4. Nov 2, 2015

### blue_leaf77

As you said, if you suppose $\mathbf{B}$ to be constant in direction and uniform, then it can be taken outside the integral.

5. Nov 2, 2015

### Nathanael

In essence, it is the same as doing this:
L1×B + L2×B + ... = (L1 + L2 + ... )×B
Which is the distrubative property of cross product.
(That's not a proof of course; I just want to make sure the idea is clear.)

6. Nov 2, 2015

### Jonathan K

This is how I arrived at my original idea, just wasn't sure if was applicable to integration.

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