Question 551: Electrostats & Capacitance

Question

Consider two charged metallic spheres S1 and
S2 of radii R1 and R2, respectively. The electric
fields E1 (on S1) and E2 (on S2) on their surfaces
are such that E1/E2 = R1/R2. Then the ratio
V1 (on S1) / V2 (on S2) of the electrostatic
potentials on each sphere is :

Accepted Answer

We know,
E
1
= $${{K{Q_1}} \over {R_1^2}}$$ and E
2
= $${{K{Q_2}} \over {R_2^2}}$$
Given
$${{{E_1}} \over {{E_2}}} = {{{R_1}} \over {{R_2}}}$$
$$ \Rightarrow $$ $${{{{K{Q_1}} \over {R_1^2}}} \over {{{K{Q_2}} \over {R_2^2}}}} = {{{R_1}} \over {{R_2}}}$$
$$ \Rightarrow $$ $${{{Q_1}} \over {{Q_2}}} = {{R_1^3} \over {R_2^3}}$$
Now $${{{V_1}} \over {{V_2}}} = {{{{K{Q_1}} \over {{R_1}}}} \over {{{K{Q_2}} \over {{R_2}}}}}$$ = $${{R_1^2} \over {R_2^2}}$$

Answer

(R1/R2)2

Answer

(R2/R1)

Answer

(R1/R2)3

Answer

R1/R2

Electrostats & Capacitance

Consider two charged metallic spheres S1 and S2 of radii R1 and R2, respectively. The electric fields E1 (on S1) and E2 (on S2) on their surfaces are such that E1/E2 = R1/R2. Then the ratio V1 (on S1) / V2 (on S2) of the electrostatic potentials on each sphere is :

Choose the correct answer: