The location from the origin where the net electric potential is zero can be determined by setting the equation for electric potentials due to both charges equal to zero and solving for the required distance.
To find the location from the origin where the net electric potential is zero due to a charge of −74pC at the origin and a charge of 12pC at 9 cm on the x-axis, we use the principle that electric potential V at a point due to a point charge q is given by V = kq/r, where k is Coulomb's constant and r is the distance from the charge to the point. At the point where the net electric potential is zero, the potential due to the −74pC charge must cancel out the potential due to the 12pC charge.
Let the required distance from the origin be d. Thus, for the -74pC charge, the potential is V1 = -k(74 × 10-12)/d and for the 12pC charge at 9 cm, the potential is V2 = k(12 × 10-12)/(9cm - d). Setting V1 + V2 = 0 yields -k(74 × 10-12)/d + k(12 × 10-12)/(9cm - d) = 0. Solving for d gives the required distance.
The point where the net electric potential due to the two charges is zero can be found by setting up an equation where the electric potentials due to each charge at that point add up to zero and solving for the distance from the origin d.