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Why any electric field doesn't exist outside the conductive spherical shell?

Physics Asked on April 28, 2021

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The conductive spherical shell(green one) and the conductive sphere are given(blue one).

The inner sphere is charged with $Q~$ and the outer shell is grounded and not charged.

$V_{text{a}}:=text{potential at the inner surface of the shell}$

$V_{text{b}}:=text{potential at the outer surface of the shell}$

$E_{r}:=text{electric field outside the shell}$

The description says that $V_{text{a}}=V_{text{b}}=E_{r}=0$

It is obvious that $V_{text{a}}=V_{text{b}}=0$ however the problem for me is to get $E_{r}=0$

For instance if we apply Gauss law and include the shell with the sphere then the below equation must be held.

$$text{sum of electric fields}=frac{Q}{epsilon_{0}}$$

What should I consider for next?

One Answer

It is because the outer sphere is grounded, so its potential difference with everything around you - assuming you are in a safely earthed environment - is zero. The outer sphere is not uncharged however. When it was connected to earth a charge -Q flowed onto its inner surface. That is another way of explaining why there is no field outside the shell: there is no net charge inside it.

Correct answer by my2cts on April 28, 2021

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