Problem 23 - Arihant AIEEE Physics

Question

Mark correct option or options: (a) A point charge can not exert force on itself (b) Coulomb's force is stronger than the gravitational force (c) Electric field can exist only in material medium (d) None of the above

Step-by-Step Solution

Answer

Correct options are (a) and (b).

Step 1: Analyzing Statement (a)

A point charge cannot exert a force on itself because it requires a second point charge to experience a force according to Coulomb's Law. Thus, statement (a) is correct.

Step 2: Analyzing Statement (b)

Coulomb's force, or the electrostatic force between charges, is significantly stronger than the gravitational force between them. Therefore, statement (b) is correct.

Step 3: Analyzing Statement (c)

Electric fields can exist in a vacuum as well as in a material medium. Therefore, statement (c) is incorrect.

Step 4: Determining the Correct Options

Since both statements (a) and (b) are true based on our analysis, the correct options are (a) and (b).

Key Concepts

Coulomb's Law

Coulomb's Law is a fundamental principle of electrostatics, which describes the force between two electric charges. Imagine two small particles, each having a charge. According to Coulomb's Law, they will exert forces on each other. The force is attractive if the charges are opposite and repulsive if the charges are alike.

The strength of this force can be described mathematically. It's directly proportional to the product of the magnitudes of each charge, and inversely proportional to the square of the distance separating them. The formula for Coulomb's Law is:

• \[F = k \frac{{|q_1 q_2|}}{{r^2}}\] where:
  • \( F \) is the electrostatic force between the charges,
  • \( q_1 \) and \( q_2 \) are the quantities of the charges,
  • \( r \) is the distance between the charges, and
  • \( k \) is Coulomb's constant, approximately equal to \( 8.99 \times 10^9 \, \text{Nm}^2/\text{C}^2 \).

Coulomb's Law only applies to point charges, which are idealized as having no size and being symmetrical. It explains that a point charge cannot exert a force on itself but needs another charge to do so.

Electric Field

The concept of the electric field is pivotal in understanding electrostatics. Think of an electric field as the space around a charged object where its electrostatic force can be experienced by other charges. It is an invisible field, but very real and measurable.

Electric fields are represented by field lines. A positive charge creates field lines that point outward, while a negative charge has field lines that point inward. The strength of an electric field, denoted by \( E \), is defined as the force \( F \) experienced per unit positive charge \( q \):

• \[E = \frac{F}{q}\] This equation helps visualize how a charge would behave when placed in an electric field, allowing predictions of force and direction.

Moreover, electric fields are not limited to existing only in materials; they can exist in the vacuum of space too. This aspect underlines their universality and essential role in the broader study of electromagnetism.

Gravitational Force Comparison

When comparing the gravitational force to the electrostatic force like that calculated by Coulomb's Law, the differences are vast. Gravitational force is the attractive pull between two masses, and it's what keeps planets orbiting and us grounded to the Earth. Newton's law of universal gravitation describes this force:

• \[F_g = G \frac{{m_1 m_2}}{{r^2}}\] where:
  • \( F_g \) is the gravitational force,
  • \( m_1 \) and \( m_2 \) are the masses involved,
  • \( r \) is the distance between the mass centers, and
  • \( G \) is the gravitational constant \( 6.674 \times 10^{-11} \, \text{Nm}^2/\text{kg}^2 \).

In essence, while gravitational force is always attractive, the electrostatic force can be either repulsive or attractive depending on the charges involved. Importantly, electrostatic forces are generally stronger than gravitational forces. This means that despite the universally present gravitational forces, electrostatic forces dominate at the atomic and molecular scales, vital in chemical reactions and interactions.