Forces gone haywire

Apr 2008
1
0
I got a few problems I haven't been able to solve after several hours now so it's time to get some help.

1. I got three equally charged particles like this

BO---------O A
!
!
O C

AB=2BC and C affects B with 4 \(\displaystyle \mu\)N

What force does A exert on B?

I have absolutely no clue as to what I need to do to solve this problem :(
 

topsquark

Forum Staff
Apr 2008
3,115
661
On the dance floor, baby!
I got a few problems I haven't been able to solve after several hours now so it's time to get some help.

1. I got three equally charged particles like this

BO---------O A
!
!
O C

AB=2BC and C affects B with 4 \(\displaystyle \mu\)N

What force does A exert on B?

I have absolutely no clue as to what I need to do to solve this problem :(
The electric force law is "inverse square." That means
\(\displaystyle F = \frac{kq_1q_2}{r^2}\)
Twice the distance implies
\(\displaystyle \frac{1}{2^2} = \frac{1}{4}\)
the force.

Another way to do this is longer, but less reliant on "hand waving."
\(\displaystyle F_{BC} = 4~\mu N = \frac{kq^2}{(BC)^2}\)

So
\(\displaystyle kq^2 = (BC)^2 \cdot (4~\mu N)\)

And we know that \(\displaystyle (AB) = 2(BC)\).

Thus
\(\displaystyle kq^2 = \left ( \frac{(AB)}{2} \right )^2 \cdot (4 \mu N)\)

\(\displaystyle \frac{kq^2}{(AB)^2} = \frac{1}{4} \cdot (4 \mu N) = 1~\mu N\)

-Dan