Question

$ABC$ is a right-angled triangle, where $AB$ and $BC$ are $25$ cm and $60cm$, respectively. A metal sphere of $2cm$ radius charged to a potential of $9\times {10}^5$ V is placed at $B$ as shown in Fig. Find the amount of work done in carrying a positive charge of $1$ coulomb from C to $A$ :

• A. $21kJ$
• B. $42kJ$
• C. $14kJ$
• D. $52kJ$

Answer 1

The correct option is B $42kJ$

$V=\frac{KQ}{r}$

$KQ=V\times r=9\times {10}^5\times 2\times {10}^{-2}$

$=18\times {10}^3$

$W=q(V_A-V_C)$

$W=1(\frac{KQ}{BC}-\frac{KQ}{AB})$

$W=1(\frac{9\times {10}^5\times 2\times {10}^{-2}}{25\times {10}^{-2}}-\frac{9\times {10}^5\times 2\times {10}^{-2}}{60\times {10}^{-2}})$

$W=42kJ$