Question

State whether the given statement is True or False :

Three positive (red) and three negative (blue) point charges are arranged symmetrically around a circle centered on point P as shown in the diagram. All point charges are of the same magnitude.

Electric Field at P will be zero while electric potential at point P will be non zero.

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Correct option is B)

Now let each charge has the magnitude q and r be the radius of circle ,

then electric field at P due to positive charges ,

$E_{′}=k(q/r_{2}+q/r_{2}+q/r_{2})=3kq/r_{2}$ , (downward)

electric field at P due to negative charges ,

$E_{′′}=k(q/r_{2}+q/r_{2}+q/r_{2)}=3kq/r_{2}$ , (downward)

net electric field at P ,

$E=E_{′}+E_{′′}=3kq/r_{2}+3kq/r_{2}=6kq/r_{2}$ (downward)

now total potential due to three positive charges at point P will be ,

$V_{′}=k(q/r+q/r+q/r)=3kq/r$ ,

total potential due to three negative charges at point P will be ,

$V_{′′}=k((−q/r)+(−q/r)+(−q/r))=−3kq/r$ ,

therefore net potential at P ,

$V=V_{′}+V_{′′}=3kq/r−3kq/r=0$

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