# Question on capacitors -- Can two charged conductors have a potential difference between them if they have equal charge?

jezza10181
Hi,

I found the following question in a physics book, and so dusted off my 30yr old knowledge on capacitors and tried to answer it. The question is as follows :-

"Suppose two nearby conductors carry the same negative charge. Can there be a potential difference between them? If so, can the definition of capacitance, C = Q/V, be used here?"

My own answer is that, yes, there can be a potential difference between the conductors, but a no to the second part. There surely cannot be a capacitance type effect between the conductors as the charges are the same, and so would repel each other and therefore not want to 'accumulate'.

What do you think?

• Delta2

Homework Helper
Gold Member
It would seem to me that each of the conductors has a capacitance, so that the voltage they each experience is proportional to the charge, (with a proportionality constant that is the inverse of the capacitance). The capacitance of the two conductors can be different, and thereby different voltages, even if the charge is the same.

• Delta2, alan123hk, sophiecentaur and 1 other person
alan123hk
"Suppose two nearby conductors carry the same negative charge. Can there be a potential difference between them? If so, can the definition of capacitance, C = Q/V, be used here?"

I think this https://www.comsol.com/blogs/how-to-calculate-a-capacitance-matrix-in-comsol-multiphysics/ is a general method to solve the capacitance problem of multi-conductor systems, but it is more complicated and abstract, and it is usually not used when dealing with simple daily engineering problems. If you are interested, you can refer to it.

Homework Helper
Gold Member
"Suppose two nearby conductors carry the same negative charge. Can there be a potential difference between them? If so, can the definition of capacitance, C = Q/V, be used here?"

My own answer is that, yes, there can be a potential difference between the conductors, but a no to the second part. There surely cannot be a capacitance type effect between the conductors as the charges are the same, and so would repel each other and therefore not want to 'accumulate'.

What do you think?
There is no potential difference between the two equally charged conductors since there is no E field between them (I am assuming two similar large plates.)

The formula C = Q/V is not wrong, it's just useless since both the numerator & denominator ## \rightarrow 0 ##.

• Delta2
Homework Helper
Gold Member
It depends on the geometry (their shape basically) of the conductors, if both have identical geometry and the same charge then there will be no potential difference. However if the two conductors have different shapes, then there will be potential difference even if they have the same charge.

• nasu
Homework Helper
Gold Member
It depends on the geometry (their shape basically) of the conductors, if both have identical geometry and the same charge then there will be no potential difference. However if the two conductors have different shapes, then there will be potential difference even if they have the same charge.
Right, but I assumed two large (very large!) plates so fringing fields are negligible and the E field is zero "everywhere".