consider an arbitrary electrostatic field configuration. A small test charge is placed at a null point ( E=0) of the configuration.show that the equilibrium of the test charge is necessarily unstable

On the contrary, assume that the equilibrium of the test charge is stable. So if the charge is displaced by a slight amount it will experience a restoring force which will bring it back to its original position, which is the null point. So all field lines near the null point must be directed inwards to the null point. This implies there is a net inward flux of electric field through a closed surface around the null point. But Gauss's Law tells that the flux through a closed surface not enclosing any charge must be zero. So here is contradiction. Thus the equilibrium of the test charge has to be unstable.

Easy Math Editor

`*italics*`

or`_italics_`

italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

`[example link](https://brilliant.org)`

`> This is a quote`

Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.`2 \times 3`

`2^{34}`

`a_{i-1}`

`\frac{2}{3}`

`\sqrt{2}`

`\sum_{i=1}^3`

`\sin \theta`

`\boxed{123}`

## Comments

Sort by:

TopNewestOn the contrary, assume that the equilibrium of the test charge is stable. So if the charge is displaced by a slight amount it will experience a restoring force which will bring it back to its original position, which is the null point. So all field lines near the null point must be directed inwards to the null point. This implies there is a net inward flux of electric field through a closed surface around the null point. But Gauss's Law tells that the flux through a closed surface not enclosing any charge must be zero. So here is contradiction. Thus the equilibrium of the test charge has to be unstable.

Log in to reply

yeah right

Log in to reply