a +35x10^-6 C point charge is placed 32 cm from an identical +32x10^-6 C charge. how much work would be required to move a +50.0x10^-6 C test charge from a point midway between them to a point 12 cm closer to either of the charges?

Question

so can you show me the work w/o the integrals. i can't really follow what you're saying.

Answer 1

It should be done with integrals, that is the basic method.

Now there is another method:

What is the potential difference between the mid point and the final point?

V= kq/r. Find the POtential from the left side, add it to the right side. q is the same, of course, 35E-6.
Then find the potential at the final point, adding the left and right contributions (Potential is a scalar, so you just add them).

Now knowing the potential difference between the final and first point, multiply that by the 50E-6 coulombs, and that will be the energy difference between the two points.

Answer 2

Yes, what he said :)