Question

In the figure there are two point charges, \(+q\) and \(-q\). There are also six positions, labeled A through \(\mathrm{F}\), at various distances from the two point charges. You will be asked about the electric potential at the different points (A through F).

A.) Rank the locations A to \(\mathrm{F}\) on the basis of the electric potential at each point. Rank positive electric potentials as higher than negative electric potentials.

For Part A.) Rank the locations from highest to lowest potential. To rank items as equivalent, overlap them.

Answer 1

Concept and reason

The potential at any point due to a point charge can be calculated using the relationship between potential, charge, and the distance between charge and the point at which the potential needs to be calculated.

Fundamentals

The potential \(\mathrm{V}\) due to a charge q at distance \(\mathrm{r}\) from the charge is given as follows:

\(V=\frac{k q}{r}\)

Here, \(\mathrm{k}\) is the Coulomb's constant. The potential is positive for a positive charge and negative for a negative charge. The potential is large at a point close to the charge because the potential is inversely proportional to the distance between the charge and the point at which potential needs to be calculated.

 

At points \(\mathrm{B}\) and \(\mathrm{E}\) the potential is higher than all the points. But the potential at point \(\mathrm{B}\) is positive, and the potential at point \(E\) is negative.

The potential at point \(\mathrm{B}\) is higher and positive because point \(\mathrm{B}\) is close to the positive charge. The potential at point \(\mathrm{E}\) is higher and negative because point \(E\) is close to negative charge.

 

The potential at point \(C\) and \(D\) is zero. Because both points \(C\) and \(D\) are at equidistant to the charges \(+q\) and \(-q\).

The points \(C\) and \(D\) are equidistant to both charges \(+q\) and \(-q\). Thus, the potential due to positive charge will cancel with potential due to negative charge at points \(\mathrm{C}\) and \(\mathrm{D}\).

 

The electric potential at points \(\mathrm{A}\) and \(\mathrm{F}\) is same. But at point \(\mathrm{A}\) the electric potential is positive, and at point \(\mathrm{F}\) the electric potential is negative. The electric potential at point \(\mathrm{A}\) is smaller than that of electric potential at point \(\mathrm{B}\) because point \(\mathrm{B}\) is closer to positive charge than point \(\mathrm{A}\). From step (1), step (2), and step (3), the ranking of points from highest potential to lowest potential is \(B>A>C=D>F>E\)

Part a The ranking from highest to lowest potential is \(B>A>C=D>F>E\).

The electric potential at point \(\mathrm{A}\) is positive because point \(\mathrm{A}\) is close to the positive charge, and the electric potential at point \(\mathrm{F}\) is negative because point \(\mathrm{F}\) is close to negative charge.