Question

Electric field outside a conducting sphere of radius $R$ carrying a charge $Q$ at a distance $x(>>R)$ from the centre is

• A. $E=\frac{Q}{4\pi {ϵ}_0{R}^2}$
• B. $E=\frac{Q}{4\pi {ϵ}_0(R^2+x^2)}$
• C. $E=\frac{Q}{4\pi {ϵ}_0{x}^2}$
• D. $E=\frac{Q}{4\pi {ϵ}_{0}xR}$

Answer 1

The correct option is C $E=\frac{Q}{4\pi {ϵ}_0{x}^2}$

Let us consider a sphere with center at center of charged sphere with radius x.

Flux through the bigger sphere=$\varphi =\frac{Q}{{ϵ}_o}$

Now,from symmetry of figure, field at all point of sphere is same and is radially outward.

And, $\varphi =\int E.dS=E\int dS=E\left(4\pi x^2\right)$

$⟹\frac{Q}{{ϵ}_o}=4\pi x^{2}E$

$⟹E=\frac{Q}{4\pi {ϵ}_o{x}^2}$

Answer-(C)