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2. Electric Potential and Capacitance
medium
Nine point charges are placed on a cube as shown in the figure. The charge $q$ is placed at the body centre whereas all other charges are at the vertices. The electrostatic potential energy of the system will be
A
Positive
B
Negative
C
Zero
D
Depends on sign and value of $q$
Solution
$v=-\frac{k Q^{2}}{a} \times 5+\frac{k Q^{2}}{a} \times 7$
$-\frac{\mathrm{k} \mathrm{Q}^{2}}{\sqrt{2} \mathrm{a}} \times 7+\frac{\mathrm{k} \mathrm{Q}^{2}}{\sqrt{2 \mathrm{a}}} \times 5+\frac{2 \mathrm{k} Q \mathrm{q}}{\frac{\sqrt{3} \mathrm{a}}{2}}$
$=\frac{2 \mathrm{k} \mathrm{Q}^{2}}{\mathrm{a}}-\frac{2 \mathrm{k} \mathrm{Q}^{2}}{\sqrt{2} \mathrm{a}}+\frac{4 \mathrm{k} \mathrm{Qq}}{\sqrt{3} \mathrm{a}}$
Standard 12
Physics
