# $\hat{\imath}$ component of force exerted on an electron by a magnetic field?

The magnetic field over a certain range is given by $\vec{B} = B_x\hat{\imath} + B_y\hat{\jmath}$, where $B_x= 4\: \mathrm{T}$ and $B_y= 2\: \mathrm{T}$. An electron moves into the field with a velocity $\vec{v} = v_x\hat{\imath}+v_y\hat{\jmath}+v_z\hat{k}$, where $v_x= 5\: \mathrm{m/s}$, $v_y= 8\: \mathrm{m/s}$ and $v_z= 9\: \mathrm{m/s}$. The charge on the electron is $-1.602 \times 10^{-19}\: \mathrm{C}$. What is the $\hat{\imath}$ component of the force exerted on the electron by the magnetic field? Answer in units of $\mathrm{N}$.

I know that $\vec{F}=q\vec{v} \times \vec{B}$, so plugging in I have:

$$\vec{F}=(-1.602 \times 10^{-19})<5,8,9> \times <4,2,0>$$

My confusion is to whether or not multiply my velocity vector components by charge (the scalar) or if I take the cross product between $\vec{B}$ and $\vec{v}$ first? I'd also like to know why whichever operation comes first does in fact come first.

• Your question is not actually dependent on the homework problem and is more general than that. You will be more likely to get a good response - and also avoid your question being closed as homework - if you remove the homework assignment and concentrate on your conceptual question. – Emilio Pisanty Dec 11 '13 at 14:39
• I didn't originally have the homework tag, just the e/m tag. Someone edited it I guess, but i'll go ahead and take it out, thank you! – Lame-Ov2.0 Dec 11 '13 at 18:33
• To be clear, I do not mean the homework tag, which is indeed appropriate at the current state of the question. I mean you should cut out all reference to the fact that this is grounded on a homework question. That makes the core concept ("do I multiply by a scalar before or after the vector product?") a lot clearer. – Emilio Pisanty Dec 11 '13 at 19:04

It doesn't matter. If you have a scalar $\alpha$ then
$$\alpha (\vec{B} \times \vec{C}) = (\alpha \vec{B}) \times \vec{C} = \vec{B} \times (\alpha \vec{C}).$$