Electrostatics – Using Symmetry in Gauss’ Law

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I have to find electric field at any inside point due to a uniformly charged solid sphere

I do it in following steps

$\to$ First I choose a spherical gaussian surface passing through required point concentric with the charged sphere.

$\to$ Next by symmetry I say that electric field will be same in magnitude at all points as all the points are equivalent to given charge distribution.

$\to$ By symmetry I say that the electric field will be directed radially.

But problem that arises is that how can I show that this field will be directed radially outwards i.e. what is the argument to prove that electric field will not be radially inwards

Best Answer

The direction of the field is given by the sign of the charge. It can be either outward or inward .