[Electrostatics] "Two charges, A and B, are placed 1.0m apart in air. P is a point midway between A and B. If the charge on A is -2.0 nC and that on B is 4.0 nC, find the electric potential at P."

Question

anonymous · Answer

I thought I could make my way to the answer by first drawing a diagram, then working out the strength of the electric fields of A and B, then working out the electric potential energy of P in each electric field separately, then work out the electric potential at P. But I realised, how can I work out the electric potential of P if it isn't a particle? I'm not sure how to approach the problem now.

anonymous · Answer

Here's an image, if it helps.

anonymous · Answer

I suggest you calculate the electric potential at point P due to A, then do the same due to charge at B, and the resultant potential is the sum.  But remember the different signs of the charges.  
The formula for electrostatic potential is similar to electric field strength, but for a radial field, it varies as 1/r (compared to 1/r squared for E. strength).

anonymous · Answer

Thanks for your reply, I'll give it another go soon.

anonymous · Answer

I'm not sure if I've done this correctly, but I took the equation for electric potential
$$V=\frac{ \Delta PE }{ q }$$
and changed PE to the equation for electric potential energy
$$V=\frac{ (Eqd) }{ q }$$
and then changed E to the equation of an eletric field
$$V=\frac{ [(\frac{ kQ }{ r^2 })qd] }{ q }$$
and plugged in the numbers. I did two of these, one for A and one for B. The electric potential at P due to A came out to be -36, and the electric potential at P due to B came out to be 72, so I added those together and got the answer of 36. I don't know if this is correct.

anonymous · Answer

The answer I got makes sense to me (but I'm still not sure if I've done it correctly), because A = -2 nC and B = 4 nC and the electric potential I got for A is half of the electric potential I got of B. Is the way I've approached the problem is stupidly complicated? Was there a simpler way to approach this?

anonymous · Answer

I used PhET's "Charges and Fields" simulation ( http://phet.colorado.edu/sims/charges-and-fields/charges-and-fields_en.html ) and I did get the answer correct! :)

anonymous · Answer

Hi, you got the answer ok.  But it looked like you're not familiar with the a standard formula for the electric potential around a point charge.  It is very similar to the one for the electric field strength, but it varies as 1/r instead:
V = kQ / r, where k = 1/(4 pi e-zero)