Question

Which of the following plots represents the variation of the electric field with distance from the centre of a uniformly charged non-conducting sphere of radius $R$ ?

• A.
• B.
• C.
• D.

Answer 1

Answer: (D)

Answer 2

The electric field intensity at a point lying outside the sphere (non-conducting) is E = $\frac{ 1}{ 4 \pi \varepsilon_0} \frac{ q}{ r^2 }$ where r is the distance of that point from centre of sphere. $\therefore E \propto \frac{ 1}{r^2}$ \hspace20mm ..( i) The electric fieid intensity at surface of sphere E = $\frac{ q}{ 4 \pi \varepsilon_0 R^2}$ or $E \propto \frac{ 1}{R^2}$ \hspace20mm ..( ii) R, being the radius of sphere. The eiectric field intensity at a point Iying inside the sphere is E = $\frac{ qr}{ 4 \pi \varepsilon_0 R^3}$ or $E \propto r$ \hspace20mm ..( iii) Also at the centre of sphere r = 0. Hence, E = 0. The graphical distribution is shown below