Two Point Charges and Magnetic Field

[Kashuno]

Homework Statement

Find the magnetic forces acting on each electron in the attached image

Homework Equations

B = \frac{μ0}{4pi}*q*\frac{v x \hat{r}}{r^{2}}
F_{m} = qv x B

The Attempt at a Solution

B_{1} = 10^{-7} * 1.6*10^{-19} * \frac{5000*10^{3}*sin(45)}{(10*10^{-10})(10*10^{-10})}
B_{1} = .057

Fm_{2} = (1.6*10^{-19})*1000*10^3*.057
Fm_{2} = 9.12*10^{-15}

Now at this point I know something is wrong, but I'm not sure what. I thought the force on the 2nd electron would be the force created by the 1st electron, but that number is definitely screaming incorrect to me. I figure it I understand how to figure out the force on 1 I can figure out the force on the other. (Electron 1 is at the bottom, electron 2 at the top). Where is my mistake?

 

[TSny]

In calculating B₁ note that r should be squared in the denominator. kilo means 10³. Are you sure you want to use 45^o for the angle in the sine function? (What is the angle between $\vec{v}$ and $\hat{r}$?)

 

[Kashuno]

Woops, don't try and do physics half asleep! Those first two errors aside, I think I see what angle I am supposed to use. The velocity of B_{1} is 45° from the x axis, but 75° from \hat{r}, since \hat{r} is along r, correct?

 

[TSny]

Looks good.