# Just understanding capacitors and e-fields

• buddingscientist
In summary, the question asks for the potential between two charged plates separated by a distance D, with one plate having excess positive charge and the other having excess negative charge. The equation given for the magnitude of the electric field between the plates is E = q/EoL, where q represents the charge and L represents the length of the plates. However, it is unclear why L is being used instead of the usual area A. The units for E are also questionable, as it should be in Newtons per Coulomb or Volts per meter instead of Newton-meters per Coulomb. It is possible that the question is assuming 1D plates and using the charge per length, lambda, to calculate E.

#### 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

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 $\lambda = \frac{q}{L}$.

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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.

## 1. What is a capacitor?

A capacitor is an electronic component that stores electrical energy by accumulating opposite charges on two conductive plates separated by an insulating material, known as a dielectric.

## 2. How does a capacitor work?

When a voltage is applied to a capacitor, one plate accumulates positive charge while the other accumulates negative charge. This creates an electric field between the plates, and the capacitor can store energy in this field. The capacitor releases this stored energy when it is connected to a circuit.

## 3. What is the unit of measurement for capacitance?

The unit of measurement for capacitance is the farad (F). However, capacitors are typically measured in smaller units such as microfarads (µF) or picofarads (pF).

## 4. How does the dielectric material affect the capacitance of a capacitor?

The dielectric material between the plates of a capacitor affects the capacitance by increasing or decreasing the strength of the electric field. A higher permittivity dielectric material will increase the capacitance, while a lower permittivity material will decrease it.

## 5. What is the difference between an electric field and an electric potential?

An electric field is a physical quantity that describes the influence of an electric charge on other charges in its vicinity. Electric potential, on the other hand, is the amount of work needed to move a unit of positive charge from one point to another in an electric field. In other words, the electric field is a vector quantity, while electric potential is a scalar quantity.