Question

A sphere of radius r carries a positive charge density (ρ) that increases linearly with radial distance r from the centre (ρ ∝ r). the radial dependence of the magnitude of electric field inside the sphere is given by

Answer 1

Question Properly :
A sphere of Radius R carries a positive charge (p) that increases linearly with radial distance x
from the centre. Then,
Electric Field Intensity inside the sphere at a point 'r 'is proportional to :
---------------------
ELECTRIC FIELD DUE TO NON -UNIFORM VOLUME CHARGE DENSITY INSIDE THE SPHERE.

Final Answer : Electric Field is proportional to
${r}^{2}$
where r is point where we have to find electric field.

Steps and Understanding :

1) We will make small spherical shells of thickness 'dx' at a distance 'x' from the centre .

2) Then, we will find Electric field due to these spherical shells at a distance 'r' from the centre .

3) Then, we get Spherical shells which are inside the spherical shell of radius' r ' will have Electric field
1/(4π£°) * dq/r^2 .

where dq is charge of small spherical shell.

4) And, Spherical shells which have radius
greater than 'r' have electric field 0 on that point 'r'.

5) So, We will integrate the dE according to our observation.
For Calculation see pic.