Four equal charges Q are placed at four corners of a square of each side a. Work done in removing a charge -Q from its centre to infinity is

Question

Four equal charges Q are placed at four corners of a square of each side a. Work done in removing a charge -Q from its centre to infinity is (A)  zero  (B)  (√2 Q2/4π ε 0a)  (C)  (√2 Q2/π ε 0a)  (D)  (Q2/2π ε 0a)

Tardigrade Admin · Accepted Answer

Potential at centre 0 of the square V0=4( (Q/4π ε 0(a/√2)) ) Work done in shifting charge from centre to infinity W=Q(V∞ -V0) W=QV0 =(4√2Q2/4π ε 0a) W=(√2Q2/π ε 0a)

Q. Four equal charges Q are placed at four corners of a square of each side a. Work done in removing a charge $- Q$ from its centre to infinity is

$zero$

$\frac{2 Q ^{2}}{4 π ε _{0} a}$

$\frac{2 Q ^{2}}{π ε _{0} a}$

$\frac{Q ^{2}}{2 π ε _{0} a}$

Potential at centre 0 of the square
$V_{0} = 4 (\frac{Q}{4 π ε _{0} ( a / 2 )})$ Work done in shifting charge from centre to infinity
$W = Q (V_{\infty} - V_{0})$
$W = Q V_{0}$
$= \frac{4 2 Q ^{2}}{4 π ε _{0} a}$
$W = \frac{2 Q ^{2}}{π ε _{0} a}$

Q. Four equal charges Q are placed at four corners of a square of each side a. Work done in removing a charge −Q from its centre to infinity is

zero

4πε0​a2​Q2​

πε0​a2​Q2​

2πε0​aQ2​