Why do charges distribute differently in metallic and insulating spheres?

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When a charge is applied to a metallic sphere, it distributes evenly across the surface due to the mobility of the charges, as explained by Gauss's Law. In contrast, charges on an insulating sphere cannot move freely, leading to potentially complex and varied charge distributions within its volume. While a uniform distribution is often assumed for simplicity, other arrangements are possible due to the restricted mobility of charges in insulators. The discussion emphasizes that the behavior of charges in metallic versus insulating spheres is fundamentally different due to the nature of charge mobility. Understanding these principles is crucial in electrostatics.
johncena
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When a charge is given to a metallic sphere it spreads in its entire surface area,and when a charge is given to an insulating sphere, it spreads over its entire volume.Why is it so?
 
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johncena said:
When a charge is given to a metallic sphere it spreads in its entire surface area,and when a charge is given to an insulating sphere, it spreads over its entire volume.Why is it so?

The latter is not always true.

You can verify the first part (changes on a sphere, under electrostatic conditions) via Gauss's Law. The charges can move and it will rearrange itself via that description.

If it is an insulating sphere, then all bets are off. The charges can have very complex charge distribution. This is because, in principle, the charges are not mobile, i.e. they can't move. So you can essentially arrange the extra charges any old way that you want. Now, in an E&M lesson, while the question can be tough, we are not malicious. So we tend to give simpler charge distribution, such as a uniform distribution throughout the volume, or a distribution that is radially symmetric. But it doesn't mean that these are the only types of distribution one can get with an insulating sphere.

Zz.
 
Yus - what he said...

You're probably taking the phrase 'a uniform sphere of charge' and adding in your own imaginary insulator - Not so?
 
For the conductors (e.g. metallic sphere),
The charges are free to move and thus they rearrange and tend to uniformly distribute over the entire surface so that each charge attains the maximum separation.

For the insulators,
The charges are restricted to move (to a certain extend) and thus they may distribute in different ways. Uniformly distributed over the entire volume is just a special case.
 
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