Chapter 20, Problem 54A

To determine

To explain: The similarity and differences between electric and gravitational forces.

Explanation of Solution

Introduction:

Electrostatic force of attraction or repulsion among the two electric charges is directly related to size of both the charges. The electrostatic force between the two charges $q_A$ and $q_B$ separated by a distance $d$ is given by Coulomb and can be written as,

  $F\text{ = K}\frac{q_A{q}_B}{d^2}$

Where $\text{ K}$ is a constant, $\text{ K}=9\times {10}^9\text{ N}{\text{.m}}^2/C^2$

Gravitational force is the attractive force between any two bodies because of the mass associated with them. It continuously tries to attract the bodies together and certainly not attempts to push them away from each other. Law of universal gravitation states that gravitational force $\left(F\right)$ between the two objects varies directly with the masses of the two objects and inversely with the square of the distance between the two objects. If $A$ and $B$ are the two objects having masses $m_A$ and $m_B$ respectively which are separated by a distance $r$ , then gravitational law can be written as,

  $F\text{ = G}\frac{m_A{m}_B}{r^2}$

Where $\text{ G}$ is gravitational constant, $\text{ K}=6.673\times {10}^{-11}\text{ N}{\text{.m}}^2/{\text{kg}}^2$

Similarities between electric and gravitational forces are − both electric and gravitational forces are proportional to the inverse of the square of the separation among the two objects and are proportional to the product of masses or product of charges of two objects.

Differences between electric and gravitational forces are − Gravitational force is always attractive in nature because mass of an object is always positive.

Electric forces are either attractive or repulsive because charges are either positive or negative. Charges of opposite polarity attracts with one another and the charges of same polarity repulses one another.