Question

Two small spheres each of radius 1 mm are kept 10 cm apart. Assuming each proton has a charge +e and each electron has a charge 0.1% less than +e then find the force between the two spheres. Density of copper is 8.9 gcm${}^{-3}$ and atomic mass number is 63.5.

• A. $1.17\times {10}^{1}2N$
• B. $2.34\times {10}^{-12}N$
• C. $1.17\times {10}^{-12}N$
• D. $2.34\times {10}^{12}N$

Answer 1

The correct option is D $2.34\times {10}^{12}N$

mass of 1 mm radius sphere
$m=8.9\times \frac{4}{3}\pi (.1{)}^3$
$=3.7\times {10}^{-2}g$
Charge on the sphere$=\frac{m}{A}{N}_{A}Z\left(\frac{0.1}{100}\right)\times$charge of $e^{+}$
$=\frac{3.7\times {10}^{-2}}{63.5}\times 6.023\times {10}^{23}\times 29\times \frac{.1}{100}\times 1.6\times {10}^{-19}$
$=1.61C$
$F=\frac{1.61\times 1.6\times {10}^{-19}\times 9\times {10}^9}{(0.1{)}^2}$
$=2.34\times {10}^{12}N$