First slide

Electrostatic potential

Question

Consider two charged metallic sphere $S_{1}$ and $S_{2}$ of radii $R_{1}$ and $R_{2}$ , respectively. The electric fields $E_{1}$ (on $S_{1}$ ) and $E_{2}$ (on $S_{2}$ ) on their surfaces are such that $E_{1} / E_{2} = R_{1} / R_{2}$ . Then the ratio $V_{1} (o n S_{1}) / V_{2} (o n S_{2})$ of the electrostatic potentials on each sphere is :

Moderate

A

$(R_{2} / R_{1})$
B

${(R_{1} / R_{2})}^{2}$
C

${(\frac{R_{1}}{R_{2}})}^{3}$
D

$R_{1} / R_{2}$

Solution

$\begin{array}{l} G i v e n : \frac{E_{1}}{E_{2}} = \frac{R_{1}}{R_{2}} \\ W e k n o w, E = k \frac{Q}{R^{2}} a n d V = k \frac{Q}{R} \\ ∴ V = E R \\ \Rightarrow \frac{V_{1}}{V_{2}} = \frac{E_{1} R_{1}}{E_{2} R_{2}} = \frac{R_{1}}{R_{2}} \times \frac{R_{1}}{R_{2}} = {(\frac{R_{1}}{R_{2}})}^{2} \end{array}$

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