# Forces gone haywire

#### dipsy34

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
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