Can you use superposition to the find potential V and the fo

Can you use superposition to the find potential V and the force F at different locations? Consider two separate systems, each with four charges of magnitude q arranged in a square of length L as shown above. Points a and c are in the center of their squares while points b and d are halfway between the lower two charges. Select all statements that are true: The electric potential at a is zero. The electric potential at b is zero. The electric potential at c is zero. The force on a positive test charge q_0 at b is zero. The force on a positive test charge q_0 at c is zero. The electric potential at d is zero. The force on a positive test charge q_0 at a is zero. The force on a positive test charge q_0 at d is zero.

Solution

Electric potential at a distance r, due to a charge q is defined as = Kq/r,

Electric force between two charges q1 & q2 kept at distance r, is defined as = Kq₁q₂/r²,

(1) At point a, both +q and both -q charge will exert equal potential, but opposite in sign. So net potential is zero True

(2)At point b, lower +q and -q charge will exert equal potential, but opposite in sign. Also upper +q and -q charge will exert equal potential, but opposite in sign. So net potential is zero True

(3) At point c, 2 pair of +q and -q charge will exert equal potential. Potential due to +q will be positive while due to -q will be negative. So net potential is zero True

(4)Force on a positive charge at b due to lower set of +q and -q charge will be equal and direction will be towards lower -q charge.So they will not cancel. Force on the same test charge at b due to upper set of +q and -q charge will be same and their net direction will be towards lower +q. Net field will be towards lower -q. False

(5)Force on a postive charge at c due to both lower +qs will be towards upper -qs charges. And the net direction will be upwards vertical. False

(6)Both lower +qs are closer to d point than both -qs. So net potential at d will not be zero. False

(7)Force at a, due to both +q will be directly away from each charge. So it will be equal and opposite in sign.Force at a, due to both -q will be directly towards each charge. So it will be equal and opposite in sign.So net force is zero. True

(8)Force at d, due to lower set of +q charges will be equal and opposite in sign.So will cancel each other.However force at d, due to upper set of -q charges, only horizontal components will cancel each other while vertical will add up. So net field will be in vertical upward. False