Question

Two charged spheres of radius $R_1$ and $R_2$ respectively, are charged and joined by a wire. The ratio of electric field of the spheres is

• A. $\frac{R_1}{R_2}$
• B. $\frac{R_2}{R_1}$
• C. $\frac{R_1^2}{R_2^2}$
• D. $\frac{R_2^2}{R_1^2}$

Answer 1

The correct option is B $\frac{R_2}{R_1}$

Two charged conducting sphere of radii r₁ and r₂ respectively connected to each other by a wire.

so, capacitance of 1st sphere , $C₁=4\pi \epsilon ₀r₁$

capacitance of 2nd sphere , $C₂=4\pi \epsilon ₀r₂$

After connecting , transfer of charge from higher potential sphere to lower potential sphere and finally, potential of both sphere will be equal .Let final potential is $V$

Now, charge at 1st sphere, $Q₁=C₁V=4\pi \epsilon ₀r₁V$

charge at 2nd sphere ,$Q₂=C₂V=4\pi \epsilon ₀r₂V$

so, ratio of charge $=Q₁/Q₂=4\pi \epsilon ₀r₁V/4\pi \epsilon ₀r₂V=r₁/r₂-------\left(1\right)$

Now, ratio of electric field $=E₁/E₂=KQ₁/r₁²/KQ₂/r₂²=Q₁r₂²/Q₂r₁²$

$E₁/E₂=Q₁/Q₂r₂²/r₁²$

Put equation (1)

$E₁/E₂=r₂/r₁$

Hence, the option $B$ is the correct answer.