Question

Two chrges $5\mu \text{C}$ and $4\mu \text{C}$ are separated by a distance $20\text{cm}$ in air work to be done to decrease the distance to $10\text{cm}$ is

• A. $0.9\text{J}$
• B. $1.8\text{J}$
• C. $9\text{J}$
• D. $18\text{J}$

Answer 1

The correct option is A $0.9\text{J}$

Given, $q_1=5\mu \text{C}{q}_2=4\mu \text{C}{r}_1=20\text{cm}=20\times {10}^{-2}\text{m}{r}_2=10\text{cm}=10\times {10}^{-2}\text{m}$

Work done $W=\Delta U$

$U_i=\frac{1}{4\pi {\epsilon }_0}\frac{q_1{q}_2}{r_1}$

$=\frac{9\times {10}^9\times 5\times {10}^{-6}\times 4\times {10}^{-6}}{20\times {10}^{-2}}$

$=9\times {10}^{-1}\text{J}=0.9\text{J}$

$U_f=\frac{1}{4\pi {\epsilon }_0}\frac{q_1{q}_2}{r_2}$

$=\frac{9\times {10}^9\times 5\times {10}^{-6}\times 4\times {10}^{-6}}{10\times {10}^{-2}}$

$U_f=18\times {10}^{-1}\text{J}=1.8\text{J}$

$W=U_f-U_i$

$=1.8-0.9=0.9\text{J}$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, (a) is the correct answer.