# Work required to move charge

1. May 18, 2009

### indie452

1. The problem statement, all variables and given/known data

situation:
there are two charges (+q) one at one corner of an equilateral triangle the other at another corner. the triangle has sides length a.

what is the work required to bring another charge (+q) in from infinity to the other corner on the equilateral triangle.

3. The attempt at a solution

ok so i know dW = -dU = F.dl

i thought that maybe finding (F) at the corner that we are bringing the charge to may help...this is:
Fc [at corner] = q2 / 2*pi*epsilon*a2

then i could just integrate this over the distance i am moving it with respect to a...however i know that the one limit will be $$\infty$$ however i dont know what the other will be

thanks for any help

Last edited: May 18, 2009
2. May 18, 2009

### LowlyPion

Consider the Voltage at the point from each of the 2 other charges.

V = k*q / r

Since work = q*ΔV

and V = 0

Then

Work = q*ΣV

3. May 18, 2009

### indie452

ok so
the E at the point is 2q / 4*pi*epsilon*a2
the V at the point is 2q / 4*pi*epsilon*a

so work to bring in point is = q(2q / 4*pi*epsilon*a) = q2 / 2*pi*epsilon*a

4. May 18, 2009

### LowlyPion

Looks like it.

Though E is a vector, don't forget, and V is a scalar here. In your first equation then the E would need to be added as vectors. Whereas for V you are adding scalars.

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/mulpoi.html#c1

5. May 18, 2009

ok thanks...