Question

Three positive (red) and three negative (blue) point charges are arranged symmetrically around a circle centered on point P as shown in the diagram below. All point charges are of the same magnitude.
Which table gives the best description of the electric field at point P and the electric potential at point P?

• A. Electric Field at P - Electric Potential at P, Zero - Zero
• B. Electric Field at P - Electric Potential at P, downward - downward
• C. Electric Field at P - Electric Potential at P, upward - positive
• D. Electric Field at P - Electric Potential at P, downward - Zero
• E. Electric Field at P - Electric Potential at P, upward - Zero

Answer 1

The correct option is D Electric Field at P - Electric Potential at P, downward - Zero

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 positive charges ,

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

electric field at P due to negative charges ,

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

net electric field at P ,

$E=E^{\prime }+E^{\prime \prime }=3kq/r^2+3kq/r^2=6kq/r^2$ (downward)

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

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

total potential due to three 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 ,

$V=V^{\prime }+V^{\prime \prime }=3kq/r-3kq/r=0$