Question 435: Electrostatics & Capacitance

Question

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 :

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

(R
1
/R
2
)
2

Answer

(R
2
/R
1
)

Answer

(R
1
/R
2
)
3

Answer

R
1
/R
2

Electrostatics & Capacitance

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 :

Choose the correct answer: