Component form of magnetic field

[mgoff87]

A 2.0 m long wire carries a current of 8.2 A and is immersed within a uniform magnetic field B.
When this wire lies along the +x axis, a magnetic force F= (-2.2 j)N acts on the wire, and when it lies on the +y axis, the force is F = (2.2 i -4.2k)N.

I saw through inspection that B in the y direction is 0, but I'm having difficulties with the x and z direction.

I know the equation in F=ILBsin(theta) and that i might need to use a dot product, but I'm stuck after that...

 

[Jame]

The force generated from a magnetic field is in the direction of the cross product of the current and the magnetic field itself. Remembering that you should easily be able to figure ot the direction of the B-field in these two cases separately, do some vector work and get the answer. I think it helps to imagine the vector arrows for the force and magnetic field, and then imagine a vector arrow perpendicular to both of those to see what you have to calculate.

 

[mgoff87]

I figured it out...all i needed to do was set it up as a matrix and find the determinate(ie the cross product) and everything worked out fine!