Eight charges having values as shown in figure are arranged symmetrically on a circle of radius 10 cm in air. The potential at the centre O is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → $2.43 × 10^6 V$
Potential at centre: $V=\frac{1}{4\pi\varepsilon_0}\cdot\frac{Q_{\text{net}}}{r}$
Sum of charges: $Q_{\text{net}}=(-7-1-5+3+10+15+7+5)\,\mu\text{C}=27\,\mu\text{C}=27\times10^{-6}\,\text{C}$
Radius $r=10\ \text{cm}=0.1\ \text{m}$ and $ \frac{1}{4\pi\varepsilon_0}=9\times10^{9}\ \text{N·m}^2\!/\text{C}^2$
$V=9\times10^{9}\cdot\frac{27\times10^{-6}}{0.1}=2.43\times10^{6}\ \text{V}$
Answer: $2.43\times10^{6}\ \text{V}$