Coulomb Law and Vectors - How do you find a scalar answer from the vector form?

[bmarson123]

Coulomb Law and Vectors - How do you find a scalar answer from the vector form??

Two small metal spheres carry equal charges q. They are located at positions r₁ = (1,1,0) nm and r₂ = (0,0,0) nm and feel a repulsive force of magnitude (mod) F = 0.05 N

How much charge is on each sphere?

Write down the force on the charge at r₂ in vector form.

What is the potential energy contained in this arrangement of charges?

Homework Equations

F₂₁ = K q₁q₂ / r₂₁³ * r₂₁

The Attempt at a Solution

First I thought I needed to convert everything into standard measurements, so metres.

But then when I put things into the equation I thought maybe stuff canceled out. But I figure I can't use F = 0.05N directly because in this equation F is a vector?

Anyway what I did was...

0.05 = K 2q / [(1,1,0) - (0,0,0)]³ * [(1,1,0) - (0,0,0)]

Then said that the vectors top and bottom cancel out so got...

0.05 = 2qk

which gave q = 2.8 x 10 ^-13 C

I didn't have a clue where to start with the rest of the question!

 

[ideasrule]

F₂₁ = K q₁q₂ / r₂₁³ * r₂₁

The r21^3 in the denominator should really be |r21|^3: the cube of the absolute magnitude of the distance between the two charges. The equation would then give you the force exerted as a vector.

However, you don't really care about the direction of the force; all you know is the magnitude, which is 0.05N. So you should use F=kq1*q2/r^2, where r is just the distance between the two charges. Note that it's q1*q2, not q1+q2!