Question

State whether the given statement is True or False :

Six negative point charges are arranged symmetrically around a circle centered at point P as shown in the diagram below. All points charges are of the same magnitude.
Electric Field at P will be zero while electric potential at point P will be non zero.

• A. True
• B. False

Answer 1

The correct option is A True

We know that electric field lines goes from positive charge to negative charge , as the total positive charge is upside of the circle and negative charge is downside of the circle therefore the direction of electric field will be downward while field lines are passing through point P .

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

then electric field at P due to upside negative charges ,

$E^{\prime }=k(q/r^2+q/r^2+q/r^2)=3kq/r^2$ , (upward)

electric field at P due to downside negative charges ,

$E^{\prime \prime }=k(q/r^2+q/r^2+q/r^{2)}=3kq/r^2$ , (downward)

net electric field at P ,

$E=E^{\prime }-E^{\prime \prime }=3kq/r^2-3kq/r^2=0$

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

$V^{\prime \prime }=k\left(\right(-q/r)+(-q/r)+(-q/r\left)\right)=-3kq/r$ ,

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

$V^{\prime \prime }=k\left(\right(-q/r)+(-q/r)+(-q/r\left)\right)=-3kq/r$ ,

therefore net potential at P ,

$V=V^{\prime }+V^{\prime \prime }=-3kq/r-3kq/r=-6kq/r$