Question

$8$ charges are arranged on a circle of radius $0.1\text{m}$ as shown. The potential at centre of the circle will be

• A. $117\times {10}^4\text{J/C}$
• B. $234\times {10}^4\text{J/C}$
• C. $351\times {10}^4\text{J/C}$
• D. $520\times {10}^4\text{J/C}$

Answer 1

The correct option is A $117\times {10}^4\text{J/C}$

Given that,
Radius of the circle, $r=0.1\text{m}={10}^{-1}\text{m}$
Electric potential is a scalar quantity. The total potential at the centre of the circle will be the sum of individual potential due to all the charges.

$V=V_1+V_2+V_3+V_4+V_5+V_6+V_7+V_8$
$V=\frac{k}{r}\{q_1+q_2+q_3+q_4+q_5+q_6+q_7+q_8\}$
$V=\frac{k}{r}\{3+10-11+11-7+7-5+5\}\mu \text{C}$
$V=\frac{k}{r}\times 13\mu \text{C}$
$V=\frac{9\times {10}^9\times 13\times {10}^{-6}}{{10}^{-1}}$
$V=117\times {10}^4\text{J/C}$

$\begin{array}{c}\text{Why this question ?}\\ \text{Tip: To find potential, we can simply}\\ \text{find the net charge of the system}\\ \text{instead to finding individual potential.}\end{array}$