Question

Where the electric field is zero?

Answer 1

Never, if the particle in the electric field has a charge.
Always, if the particle has no overall charge.

Explanation:

Electric field is usually given by:
`E=V/d=F/Q_2=(kQ_1)/r^2`, where:

• `E` = Electric field strength (`NC^-1 or Vm^-1`)
• `V` = electric potential
• `d` = distance from the point charge (`m`)
• `F` = Electrostatic force (`N`)
• `Q_1 and Q_2` = charge on objects `1` and `2` (`C`)
• `r` = distance from point charge (`m`)
• `k` = `1/(4piepsilon_0)=8.99*10^9Nm^2C^-2`
• `epsilon_0` = permittivity of free space (`8.85*10^-12` `Fm^-1`)

However, depending on where the electric field is, a different value would be used instead of `epsilon_0`.

Given `E=(kQ)/r^2`, `E!=0` when `Q>0`. This can be shown by doing `r=sqrt((kQ)/E)`. Putting `E=0` gives a value for `r` as `text(undefined)`.

So, unless the particle in the electric field has no charge, then the electric field will always have a value.