Question

A 7.80-nC charge is located 1.70 m from a 4.30-nC point charge.

(a) Find the magnitude of the electrostatic force that one charge exerts on the other.

(b) Is the force attractive or repulsive?

 

Answer 1

Concepts and reason

The concept required to solve the given question is electrostatics due to different charges. Initially, calculate the magnitude of the electrostatic force that one charge exerts on the other. Finally, find whether the force is attractive or repulsive in nature.

Fundamentals

The expression for the electrostatic force is as follows:

\(F=\frac{k q_{1} q_{2}}{r^{2}}\)

Here, \(\mathrm{k}\) is the permittivity of free space, \(r\) is the separation between the two charges, \(q_{1}\) is the charge on the first point, and

\(q_{2}\) is the charge on the second point.

Substitute \(9 \times 10^{9} \mathrm{~N} \cdot \mathrm{m}^{2} \cdot \mathrm{C}^{-2}\) for \(\mathrm{k}, 7.80 \mathrm{nC}\) for \(q_{1}, 4.30 \mathrm{n} \mathrm{C}\) for \(q_{2}\), and \(1.70 \mathrm{~m}\) for \(r\) in the equation \(F=\frac{k q_{1} q_{2}}{r^{2}}\).

$$ \begin{array}{c} F=\frac{\left(9 \times 10^{9} \mathrm{~N} \cdot \mathrm{m}^{2} \cdot \mathrm{C}^{-2}\right)(7.80 \mathrm{nC})(4.30 \mathrm{nC})}{(1.70 \mathrm{~m})^{2}} \\ =\frac{\left(9 \times 10^{9} \mathrm{~N} \cdot \mathrm{m}^{2} \cdot \mathrm{C}^{-2}\right)(7.80 \mathrm{nC})\left(\frac{10^{-9} \mathrm{C}}{\mathrm{T} .00 \mathrm{CC}}\right)(4.30 \mathrm{nC})\left(\frac{10^{-9} \mathrm{C}}{1.00 \mathrm{nC}}\right)}{(1.70 \mathrm{~m})^{2}} \\ =104.3 \times 10^{-9} \mathrm{~N} \\ =104.3 \mathrm{nN} \end{array} $$

According to Coulomb's law, the electrostatic force of attraction is directly proportional to the product of the two charges and inversely proportional to the square of the distance between the charges. Thus, the value of Coulomb's constant is \(9 \times 10^{9} \mathrm{~N} \cdot \mathrm{m}^{2} \cdot \mathrm{C}^{-2}\).

Both the charges \(q_{1}\) and \(q_{2}\) are positive in sign, that is, both the charges are positive. And according to the properties of Coulomb's force, the charges with the same sign repel each other, and the charges with opposite signs attract each other. Thus, the force is repulsive.

According to the property of the electrostatic force, the charges with the same sign are repulsive in nature, and the charges with the opposite signs are attractive in nature.

Part A The magnitude of the electrostatic force that one charge exerts on the other is equal to104.3nN.

Part B The force is repulsive in nature.