JEE PYQ: Electrostatics Question 32
Question 32 - 2020 (08 Jan Shift 2)
Consider two charged metallic spheres $S_1$ 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 $V_1$(on $S_1$)/$V_2$(on $S_2$) of the electrostatic potentials on each sphere is:
(1) $R_1/R_2$
(2) $(R_1/R_2)^2$
(3) $(R_2/R_1)$
(4) $\left(\frac{R_1}{R_2}\right)^3$
Show Answer
Answer: (2)
Solution
$E = \frac{kQ}{R^2}$ and $V = \frac{kQ}{R}$, so $V = ER$. Given $\frac{E_1}{E_2} = \frac{R_1}{R_2}$: $\frac{V_1}{V_2} = \frac{E_1 R_1}{E_2 R_2} = \frac{R_1}{R_2} \cdot \frac{R_1}{R_2} = \left(\frac{R_1}{R_2}\right)^2$.
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