Question

In the rectangle, the two corners have charges $q_1=-8\mu C$ and $q_2=+4\mu C$. The work done in moving a charge $+3\mu C$ from B to A

• A. $3.2J$
• B. $4.9J$
• C. $5.6J$
• D. $4.2J$

Answer 1

Answer: (B)

Potential at A
$V_A=\frac{K{q}_1}{r}+\frac{K{q}_2}{r}$
$V_A=K\left[\frac{-8\times 10^{-6}}{20\times 10^{-2}}+\frac{4\times 10^{-6}}{5\times 10^{-2}}\right]$
$V_A=K\times 10^{-4}[-0.4+0.8]$
$V_A=0.4\times K\times 10^{-4}V$
Potential at $B{V}_B=\frac{K{q}_1}{r}+\frac{K{q}_1}{r}$
$V_B=K\left[\frac{4\times 10^{-6}}{20\times 10^{-2}}-\frac{8\times 10^{-6}}{5\times 10^{-2}}\right]$
$V_B=K\times 10^{-4}[0.2-1.6]$
$V_B=-1.4K\times 10^{-4}V$
Charge move from $B$ to $A$ then
$W=q\left(V_A-V_B\right)$
$W=3\times 10^{-6}\left(0.4K\times 10^{-4}-\left(-1.4K\times 10^{-4}\right)\right)$
$\therefore W=3\times 10^{-6}\times 1.8\times 9\times 10^{-4}$
$W=48.6\times 10^{-1}$
$=4.86J\approx 4.9J$