Question 730: Electrostatics & Capacitance

Question

Two charged spherical conductors of radius R
1
and R
2
are connected by a wire. Then the ratio of surface charge densities of the spheres ($$\sigma$$
1
/ $$\sigma$$
2
) is :

Accepted Answer

$${Q_1} = {{\sum Q } \over {{R_1} + {R_2}}} 	imes {R_1}$$
$${Q_2} = {{\sum Q } \over {{R_1} + {R_2}}} 	imes {R_2}$$
$${\sigma _1} = {{{Q_1}} \over {4\pi R_1^2}} = {{\sum Q } \over {{R_1} + {R_2}}} 	imes {{{R_1}} \over {4\pi R_1^2}} \propto {1 \over {{R_1}}}$$
$${\sigma _2} = {{{Q_2}} \over {4\pi R_2^2}} = {{\sum Q } \over {{R_1} + {R_2}}} 	imes {{{R_2}} \over {4\pi R_2^2}} \propto {1 \over {{R_2}}}$$
$${{{\sigma _1}} \over {{\sigma _2}}} = {{{R_2}} \over {{R_1}}}$$

Answer

$${{R_1^2} \over {R_2^2}}$$

Answer

$${{R_1^{}} \over {R_2^{}}}$$

Answer

$${{R_2^{}} \over {R_1^{}}}$$

Answer

$$\sqrt {\left( {{{{R_1}} \over {{R_2}}}} \right)} $$

Electrostatics & Capacitance

Two charged spherical conductors of radius R 1 and R 2 are connected by a wire. Then the ratio of surface charge densities of the spheres ($\sigma 1 / \sigma$ 2 ) is :

Choose the correct answer: