Question

Six negative 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, zero - negative
• C. Electric Field at P - Electric Potential at P, downward - downward
• D. Electric Field at P - Electric Potential at P, downward - negative
• E. Electric Field at P - Electric Potential at P, negative - zero

Answer 1

The correct option is B Electric Field at P - Electric Potential at P, zero - negative

Magnitude of electric field at point P due to one charge $E=\frac{kq}{r^2}$

Due to symmetry, electric field due to charge 1 is cancelled by electric field due to charge 4.

Similarly, E.F by 2 cancels E.F by 5 and E.F by 3 cancels E.F by 6.

Hence net electric field at point P is zero i.e $E_p=0$

Potential at point P due to one charge $V_1=\frac{-kq}{r}$

$\therefore$ Net potential at point P due to six charges $V_p=6V_1=\frac{-6kq}{r}$

Hence option B is correct.