Question

Consider two charges located on a line in a region far from other charges. Charge 1 is located at position x = 0 m on the line, and Charge 2 is located at position x = 12 m on the line.
A proton placed at any point on the line between the two charges will experience a net force due to the two charges. The net force acting on the proton is shown as a function of position in the graph, where positive values of force represent rightward force.
What is the sign of each charge, and which charge is stronger?

• A. Charge 1 is positive, Charge 2 is negative, and the stronger charge is Charge 1.
• B. Charge 1 is positive, Charge 2 is negative, and the stronger charge is Charge 2.
• C. Charge 1 is positive, Charge 2 is positive, and the stronger charge is Charge 2.
• D. Charge 1 is negative, Charge 2 is negative, and the stronger charge is Charge 1.
• E. Charge 1 is positive, Charge 2 is positive, and the stronger charge is Charge 1.

Answer 1

Answer: (A)

Charge 1 is positive, Charge 2 is negative, and the stronger charge is Charge 1.

The Coulomb force experienced by a charged particle is $\frac{1}{4\pi {ϵ}_0}\frac{Qq}{d^2}$.

where $q,Q$ are the respective charges and $d$ is the separation between them.

Since force is positive in the left part of the curve, the charge placed at $x=0m$ is positive. Since the force is negative in right half of the curve, the charge placed at $x=12m$ is negative.

The net force at a point is resultant of the two forces at that point. Since at the exact mid-point where $d$ of both the curves is same(at $x=6m$), the net force at that point is positive.

Hence $\left|Q_{+}\right|>\left|Q_{-}\right|$