Four electric charges +q,+q,-q and -q are placed at the corners of a square of side 2 ~L (see figure). The electric potential at point A , mid-way between the two charges +q and +q , is

Correct answer: B. (1)/(4 π _0) (2 q)/(L)(1- 1 5 ) V=(1)/(4 π _0) (q)/(r) Here, aligned & V=2 V_ +ve +2 V_ -ve & V=(1)/(4 π _0)[(2 q)/(L)- 2 q L 5 ] & V=(2 q)/(4 π _0 L)(1- 1 5 ) aligned

NEET 2011

Exam: NEET
Year: 2011
Subject: Physics
Chapter: Electrostatics

NEET 2011 · Physics · Electrostatics

Four electric charges +q,+q,-q and -q are placed at the corners of...

Four electric charges

+q,+q,-q

and

-q

are placed at the corners of a square of side

2 \mathrm{~L}

(see figure). The electric potential at point

A

, mid-way between the two charges

+q

and

+q

, is

Four electric charges +q,+q,-q and -q are placed at the corners of a square of side 2 ~L (see figure). The electric

Options

A $\frac{1}{4 \pi \varepsilon_0} \frac{2 q}{L}\left(1+\frac{1}{\sqrt{5}}\right)$
B $\frac{1}{4 \pi \varepsilon_0} \frac{2 q}{L}\left(1-\frac{1}{\sqrt{5}}\right)$
Czero
D $\frac{1}{4 \pi \varepsilon_0} \frac{2 q}{L}(1+\sqrt{5})$

Correct answer

B. $\frac{1}{4 \pi \varepsilon_0} \frac{2 q}{L}\left(1-\frac{1}{\sqrt{5}}\right)$

Step-by-step solution

V=\frac{1}{4 \pi \varepsilon_0} \frac{q}{r}

Here,

\begin{aligned} & V=2 V_{+\mathrm{ve}}+2 V_{\text{-ve }} \\ & V=\frac{1}{4 \pi \varepsilon_0}\left[\frac{2 q}{L}-\frac{2 q}{L \sqrt{5}}\right] \\ & V=\frac{2 q}{4 \pi \varepsilon_0 L}\left(1-\frac{1}{\sqrt{5}}\right) \end{aligned}

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