Question

A neutral sphere of radius r and density ρ is intended to be suspended with an electric field E existing on the earth's surface directed vertically up. What fraction of the electrons should be removed from the sphere. Given that, the atomic number and atomic mass of the material of the sphere are Z & A respectively. Avogadro number is N_A. Assume that the sphere is able to hold the necessary charge without any leakage-

• A.
• B. $\frac { 3 \mathrm { gA } } { \mathrm { eEZ } }$
• C. $\frac { \mathrm { gA } } { \mathrm { eEZN } _ { \mathrm { A } } }$
• D. $\frac { 2 \mathrm { gA } } { \mathrm { eEZN } _ { \mathrm { A } } }$

Answer 1

Answer: (C)

$\frac { \mathrm { gA } } { \mathrm { eEZN } _ { \mathrm { A } } }$

Answer 2

mg = qE

mg = n e E

$\frac { 4 } { 3 }$πr³ × ρ × g = n e E

n =

Number of moles of the metal in sphere = $\frac { \mathrm { m } } { \mathrm { A } }$

= $\frac { 4 } { 3 } \frac { \pi r ^ { 3 } \rho } { \mathrm { A } }$

Number of metal atoms = $\frac { 4 } { 3 } \frac { \pi \mathrm { r } ^ { 3 } \rho \times \mathrm { N } _ { \mathrm { A } } } { \mathrm { A } }$

Total number of electrons = = N Say

Required fraction =