Two charged conducting spheres and of radii 8 cm and 18 cm are connected to each other by a wire

Question

Two charged conducting spheres $S_{1}$ and $S_{2}$ of radii 8 cm and 18 cm are connected to each other by a wire. After equilibrium is established, the ratio of electric fields on $S_{1}$ and $S_{2}$ spheres are $E_{S_{1}}$ and $E_{S_{2}}$ respectively. The value of $\frac{E_{S_{1}}}{E_{S_{2}}}$ is _______. [2026]

Smart Achievers · Accepted Answer

(4)

$At equilibrium: V_{1} = V_{2}$

$\frac{k Q_{1}}{8} = \frac{k Q_{2}}{18}$ ${V_{surface} = \frac{k Q}{R}}$

$\Rightarrow \frac{Q_{1}}{Q_{2}} = \frac{4}{9}$

$\frac{E_{S_{1}}}{E_{S_{2}}} = \frac{k Q_{1}}{r_{1}^{2}} \frac{r_{2}^{2}}{k Q_{2}}$ ${E_{surface} = \frac{k Q}{R^{2}}}$

$\frac{E_{S_{1}}}{E_{S_{2}}} = \frac{Q_{1}}{Q_{2}} {(\frac{r_{2}}{r_{1}})}^{2} = \frac{4}{9} \times {(\frac{9}{4})}^{2} = \frac{9}{4}$

Solution

1 $\frac{3}{2}$

2 $\frac{2}{3}$

3 $\frac{4}{9}$

4 $\frac{9}{4}$

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Solution

Q. Two charged conducting spheres S1 and S2 of radii 8 cm and 18 cm are connected to each other by a wire. After equilibrium is established, the ratio of electric fields on S1 and S2 spheres are ES1 and ES2 respectively. The value of ES1ES2 is _______. [2026]

1 32

2 23

3 49

4 94

Ans. (4) At equilibrium: V1=V2 kQ18=kQ218 {Vsurface=kQR} ⇒Q1Q2=49 ES1ES2=kQ1r12r22kQ2 {Esurface=kQR2} ES1ES2=Q1Q2(r2r1)2=49×(94)2=94

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1 $\frac{3}{2}$

2 $\frac{2}{3}$

3 $\frac{4}{9}$

4 $\frac{9}{4}$