Calculating Magnetic Force on a Wire: Unit Vector Notation Explained

[CEHooper]

Problem:
A wire 50.0 cm long carries a 0.500 A current in the positive
direction of an x-axis through a magnetic field
→....^...^
B=(3.00mT)j + (10.0mT)k
In unit-vector notation, what is the magnetic force on the wire?

Work (so far):......→...→...→
To start, I have the formula F = iL x B, but I am hung up on how to get this into unit vector notation.

Please help. Thanks!

 

[Euge]

Hi CEHopper,

Since the wire is $0.500\, \rm{m}$ long and the current moves in the positive $x$-direction, $\vec{L} = (0.500\,\rm{m}) \hat{i}$. Since $i = 0.500\, \rm{A}$, then $i\vec{L} = (0.0025\, \rm{A}\cdot \rm{m})\vec{i}$. Take the cross product with $\vec{B} = (0.003\, \rm{T})\hat{j} + (0.010\, \rm{T})\hat{k}$ to obtain $\vec{F}$. To calculate the cross product, use the rules $\vec{a} \times (\vec{b}\times \vec{c}) = \vec{a}\times \vec{b} + \vec{a} \times \vec{c}$, $\hat{i}\times \hat{j} = \hat{k}$, and $\hat{i}\times \hat{k} = \hat{j}$.

 

[CEHooper]

Thank you!