Just understanding capacitors and e-fields

[buddingscientist]

It's a problem were we are given the usual - 2 plates separated in air, distance D apart, each of length L, one excess +ve charge the other exces -ve charge

The question then states:
the magnitude between the e-field plates is: E = q/EoL, calculate the potential (blah blah..)

My question is why have they used L?
Wouldn't this give the electric field units of: C / (C^2.N^-1.m^-2)*(m)
(apologies for no latex)
= Newton-metres per Coulomb?

when it should be Newtons per Coulomb (or Volts per metre)?

Is the question assuming 1D plates?
Just looking to get this cleared up, thanks

 

[Nick89]

I don't know why they used L either... However, you have not specified what q is. Is it a charge, thus units Coulomb? Could it be that q is a charge per length with units C/m ?

I think it's weird using the length of a capacitor plate though... It's the area that usually matters. Usually it's:
$$E = \frac{\sigma}{\epsilon_0} = \frac{Q}{\epsilon_0 A}$$ so $\sigma = \frac{Q}{A}$.

Maybe in this case $$E = \frac{q}{\epsilon_0 L} = \frac{\lambda}{\epsilon_0}$$ where $\lambda = \frac{q}{L}$.

 

[Moetasim]

It is possible that the question is assuming 1D plates, as the use of L in the equation for electric field (E=q/EoL) is typically used for parallel plate capacitors with infinitely long plates. In this case, the length L represents the distance between the plates, rather than the physical length of the plates themselves.

If the plates are not infinitely long, then the equation for electric field would be E = q/EoA, where A is the area of the plates. In this case, the units for electric field would be Newtons per Coulomb (or Volts per metre).

It is important to clarify with the question or the instructor what is meant by the length L in this context. If the plates are indeed 1D, then the units for electric field would be as you have calculated (Newton-metres per Coulomb). However, if the plates are not 1D, then using L in the equation would result in incorrect units.

In summary, it is important to carefully consider the assumptions and definitions being used in a problem related to capacitors and electric fields in order to correctly calculate and interpret the results.