Electrostatic Potential And Capacitance Ques 48
48. Four electric charges $+q,+q,-q$ and $-q$ are placed at the corners of a square of side $2L$ (see figure). The electric potential at point $A$, midway between the two charges $+q$ and $+q$, is
[2011]
(a) $\frac{1}{4 \pi \epsilon_0} \frac{2 q}{L}(1+\sqrt{5})$
(b) $\frac{1}{4 \pi \in_0} \frac{2 q}{L}(1+\frac{1}{\sqrt{5}})$
(c) $\frac{1}{4 \pi \in_0} \frac{2 q}{L}(1-\frac{1}{\sqrt{5}})$
(d) zero
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Answer:
Correct Answer: 48.(c)
Solution:
- (c) Distance of point A from the two $+q$ charges $=L$.
Distance of point A from the two $-q$ charges $=\sqrt{L^{2}+(2 L)^{2}}=\sqrt{5} L$.
$\therefore V_A=(\frac{Kq}{L} \times 2)-(\frac{Kq}{\sqrt{5} L} \times 2)$
$=\frac{2 Kq}{L}[1-\frac{1}{\sqrt{5}}]$
$=\frac{1}{4 \pi \epsilon_0} \cdot \frac{2 q}{L}(1-\frac{1}{\sqrt{5}})$
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