A shpere of radius `r` carries a surface charge a density `sigma = ar`, where a is a constant, vector and `r` is radius vector of a point of the sphere ralative to its centre. Find the electric field strength vector at the centre relative at the centrre of the sphere.

Explanation

To find the electric field strength vector at the center of a sphere with a surface charge density given by \(\sigma = \mathbf{a} \cdot \mathbf{r}\), where \(\mathbf{a}\) is a constant vector and \(\mathbf{r}\) is the radius vector, we can follow these steps:

### Step 1: Understand the Charge Density
The surface charge density is given by:
\[ \sigma = \mathbf{a} \cdot \mathbf{r} \]
This indicates that the charge density varies with the position on the sphere's surface.
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