Question # Four charges are placed at the corners of a square of side ( a )

# Four charges are placed at the corners of a square of side ( a )

Work done by external agent in carrying an electron from point 0 to ( 0^{prime} ) is

(1) ( frac{-4 e k Q}{a}(sqrt{5}-2 sqrt{2}) )

(2) ( frac{4 e k Q}{a}(sqrt{5}-2 sqrt{2}) )

(3) ( frac{4 e k Q}{a}(sqrt{5}+2 sqrt{2}) )

(4)( quad frac{-4 e k Q}{a}left[1+frac{1}{sqrt{5}}-sqrt{2}right] )

Solution

Potential at Point

[

begin{array}{l}

v_{0}=4 x^{k q} sqrt{2}=frac{4 sqrt{2} k q}{a}

v_{d}=frac{2 k k q}{a}+2 x frac{k q}{sqrt{5} a}

end{array}

]

[

V_{0^{prime}}=frac{4 k q}{a}left(frac{sqrt{s}+1}{sqrt{5}}right)

]

-2

[

w=-(-e)left[v_{0}^{prime}-v_{0}right]<-u_{0} e e q^{n}(0)(2)

]