# Electrostatics and Coulumb's law, potentials and test charges

1. Feb 9, 2013

### Plasmosis1

I am given 4 potential charges, 1V, 3V, -6V, and 5V, all arranged randomly around each other. There is a test charge located at infinity. No distances are given between the potentials.

1. Where will a test charge of 2*10^-6 C travel?
2. What is its kinetic energy?
3. Find the capatinance of a capacitor with the same energy as #2
4. Use a -2*10^-6 C test charge instead on the +2*10^-6 C charge. Where will it go?
5. If the new charge has a mass of 37.3*10^-21 what will its speed be at its destination?

1. I think it will go towards the -6 potential
2. PE= q*v and I think the PE will equal the KE when it arrives. 2*10^-6*(1+5+(-6)+3)=6*10^-6. However I'm not sure if I should add the volts together.
3. C=q/v so 2*10^-6/(1+5+(-6)+3)=6.67*10^-7 F. Again, I'm not sure if I should add the volts together.
4. I would think the charge would stay in infinity because it has an opposite charge.
5. I have no clue on this question because it contradics my previous answer.

I don't really have any idea what I'm doing so any help would be appreciated.

2. Feb 12, 2013

### ehild

You mean that there are four charged objects (small metal spheres, for example) held at different potentials (with respect to infinity).
1.) Yes, the positive test charge will go to the negatively charged object.
2.) The test charge had zero kinetic energy and zero potential energy at infinity. Arriving to the place where the potential is -6 V, its potential energy is PE=UQ=-6*2˙10-6=-12˙10-6 J. As the energy is conserved in an electric field, KE=12˙10-6 J. The other charged objects do not matter as the potential is given at the place where the test charge arrives. Do not add the potentials.
3.) You have to find the a capacitance if the capacitor has the same energy as the KE of the test charge. How is the energy of a capacitor expressed in terms of its capacitance and voltage?
4.) When the test charge is negative it will be attracted by the objects at positive potential, and it will go to the place at highest potential.
5.)Calculate the kinetic energy again, and you get the speed from it.

ehild