Final answer:
To find the point on the x-axis where the electric field is zero, we can set up an equation involving the electric potential of each charge. Solving this equation will give us the distances from each charge to the point where the electric field is zero.
Step-by-step explanation:
In order to find the point on the x-axis where the electric field is zero, we need to consider the electric potential. The electric potential at a point is the amount of potential energy per unit charge at that point. In this case, we have a -120nC point charge and a +24.0nC point charge 13.5 cm apart on the x-axis.
To find the point where the electric field is zero, we need to find the point where the electric potential of each charge cancels out. The electric potential of a point charge is given by the equation V = q/4πε₀r, where V is the electric potential, q is the charge, ε₀ is the permittivity of free space, and r is the distance from the charge.
Since the electric field is zero, the sum of the electric potentials of the two charges must be equal to zero. So, we can set up the following equation: -120nC/4πε₀r₁ + 24.0nC/4πε₀r₂ = 0
Solving this equation will give us the values of r₁ and r₂, which represent the distances from each charge to the point where the electric field is zero.