Question

electric field at 20cm from the centre of a uniformly charged non conducting sphere of radius 10 centimetre is E. then at a distance 5 centimetre from the centre it will be

1) 16E

2) 4E

3) 2E

4) zero

Answer 1

The sphere is non conducting so there will be electric field inside it

Electric field outside is given by - KQ/R^2 where R is 20cm

Electric field inside is given by - KQx/r^2 where r is radius 10cm and x is distance from the center 5 cm

Put the values and divide you will get the answer

2E

Answer 2

Answer:

The electric field at a point of 5cm distance is $2E$

Explanation:

Given a uniformly charged non conducting sphere of radius, $R=10 cm$

        distance from the center, $r=20cm$

        electric field at distance r is E

The sphere is a uniformly charged non conducting, so the charge distribution in terms of charge density, $\rho$ is given by, $q=\frac{4}{3} \pi R^{3} \rho$

Since 20cm is greater than the radius of sphere, therefore the electric field at 20cm is given by

                           $E=k\frac{q}{r^{2} }=k\frac{q}{(20)^{2} }$ where $k=\frac{1}{4\pi \epsilon_{0} }$.  

Since 5cm is less than the radius of sphere, therefore the electric field at 5cm is given by  

                              $E_{5} =\frac{kqr}{R^{3} }=\frac{kq\times 5}{10^{3} }$

Dividing both the equations,

                              $\frac{E}{E_{5} } =\frac{\frac{kq }{20^{2} }}{\frac{kq\times 5}{10^{3} }}=\frac{\frac{1 }{20^{2} }}{\frac{5}{10^{3} }}$    

                                   $={\frac{10^{3} }{5\times 20^{2} }}=\frac{1}{2}$

Therefore, the electric field at 5cm distance is $E_{5} =2E$