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

Question

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 (A)  (1/ 4 π ε0 ) ( 2q/ L) (1 + √ 5) (B) (1/ 4 π ε0 ) ( 2q/ L) [ 1 - ( 1/ √ 5) ]  (C)  (1/ 4 π ε0 ) (1 + ( 2q/ L) (1 - (1/√ 5))) (D) zero

Tardigrade Admin · Accepted Answer

V A =( kq / L )+( kq / L )-( kq /√5 L )-( kq /√5 L ) =(2 kq / L )(1-(1/√5))

Q. 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 $A$ , midway between the two charges $+ q$ and $+ q$ , is

$\frac{1}{4 π ε _{0}} \frac{2 q}{L} (1 + 5)$

$\frac{1}{4 π ε _{0}} \frac{2 q}{L} [1 - \frac{1}{5}]$

$\frac{1}{4 π ε _{0}} (1 + \frac{2 q}{L} (1 - \frac{1}{5}))$

zero

$V_{A} = \frac{k q}{L} + \frac{k q}{L} - \frac{k q}{5 L} - \frac{k q}{5 L}$
$= \frac{2 k q}{L} (1 - \frac{1}{5})$

Q. 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

4πε0​1​L2q​(1+5​)

4πε0​1​L2q​[1−5​1​]

4πε0​1​(1+L2q​(1−5​1​))