Current on wire, three axes, magnetic force

[scholio]

Homework Statement

a 0.2 meter straight piece of wire has a current of 30 ampere flowing through it, pointing in the +z direction. the magnetic field presented in space is given by:

B = 2B_0i + 4B_0j + 3B_0k

what is the force on the wire?

Homework Equations

magnetic force on a current F = IL X B = ILBsin(theta)where X indicate cross product, I is current, L is length, B is magnetic field

The Attempt at a Solution

F = IL X B
F = ILB sin(theta)
F = (30)(0.2)(2B_0i + 4B_0j + 3B_0k) sin(90)
F = 12B_0i + 24B_0j + 18B_0k

i'm not sure sure whether i did the calculation correct, is the 30 amps only multiplied with the 3B_0k since the current points in the +z direction? i multiplied it through all, i,j,k.

will my final answer be presented in components of each axis?

 

[scholio]

couldn't edit original post, i am supposed to get -24B_0i + 12B_0j

 

[Mindscrape]

You did the cross product wrong. If the length is in the z direction than z component from the magnetic field will die out in the cross product. The cross product is the multiplication of orthogonal (perpendicular) components, so physically you should not see things going in the same direction contribute.

Do you know of the component-wise way of doing cross products? If you don't know the determinate trick, then you can just use the right hand rule and figure it out.

 

[scholio]

the determinant trick involves matrices correct? i think i know how to do that, could you explain the right hand rule a little more, having a little trouble visualizing.

 

[Mindscrape]

Okay so with the determinate trick you would have something like this

http://www.ucl.ac.uk/Mathematics/geomath/level2/mat/mat121.html

For the right hand rule you want to point your fingers in the direction of the first vector, and then curl them in the direction of the second vector. Your thumb would show you the direction of the resultant vector. For example, x cross y should show you z; or, z cross y should show -x.