Question

Two equally charged spheres of radii $a$ and $b$ are connected together. What will be the ratio of electric field intensity on their surfaces?

• A. $\frac{a}{b}$
• B. $\frac{a^2}{b^2}$
• C. $\frac{b}{a}$
• D. $\frac{b^2}{a^2}$

Answer 1

Answer: (C)

$\frac{b}{a}$

Let charge on each sphere $=q$.
When they are connected, total charge on the system $=2q$ and their potential will be equal.
Now if charge on sphere of radii a is $q_a$ , charge on sphere of radii b is $q_b=2q-q_a$.
Now $V_a=V_b\Rightarrow \frac{q_a}{4\pi {ϵ}_{0}a}=\frac{q_b}{4\pi {ϵ}_{0}b}$
$\Rightarrow \frac{q_a}{q_b}=\frac{a}{b}$
Electric field for sphere a is $E_a=\frac{q_a}{4\pi {ϵ}_0{a}^2}$ and
Electric field for sphere b is $E_b=\frac{q_b}{4\pi {ϵ}_0{b}^2}$
$\therefore \frac{E_a}{E_b}=\frac{q_a}{q_b}\frac{b^2}{a^2}=\frac{a}{b}.\frac{b^2}{a^2}=\frac{b}{a}$