Problem 117 - Master Resource Book in JEE Main Physics

Question

Assertion-Reason type. Each of these contains two Statements : Statement I (Assertion), Statement II (Reason). Each of these questions also has four alternative choice, only one of which is correct. You have to select the correct choices from the codes (a), (b), (c) and (d) given below (a) If both Assertion and Reason are true and the Reason is correct explanation of the Assertion (b) If both Assertion and Reason are true but Reason is not the correct explanation of the Assertion (c) If Assertion is true but Reason is false (d) If Assertion is false but the Reason is true Assertion Force between two charges decreases, when air separating the charges is replaced by water. Reason Medium intervening between the charges has no effect on force.

Step-by-Step Solution

Answer

Option (c): Assertion is true, but Reason is false.

Step 1: Understand the Assertion

The Assertion states that the force between two charges decreases when air is replaced by water. This is related to the concept of dielectric constant of a medium. The dielectric constant of water is greater than that of air, which means water reduces the electrostatic force between charges more than air does.

Step 2: Evaluate the Assertion

The statement is true. When air is replaced by water, the force decreases because water has a higher dielectric constant, reducing the effective force between charges.

Step 3: Understand the Reason

The Reason suggests that the medium intervening between charges has no effect on force. This is not correct as the force between charges is inversely proportional to the dielectric constant of the medium.

Step 4: Evaluate the Reason

The Reason is false. The medium does affect the force between two charges. A medium with a higher dielectric constant reduces the force between charges.

Step 5: Conclude on the Relationship between Assertion and Reason

Since the Assertion is true but the Reason is false, the correct choice is that there is no correct explanation (option c).

Key Concepts

Coulomb's Law

Coulomb's Law is a fundamental principle in physics that describes the force between two point charges. This law states that the electrostatic force (\( F \)) between two charges is directly proportional to the product of the magnitudes of the charges (\( q_1 \) and \( q_2 \)) and inversely proportional to the square of the distance (\( r \)) between them. The mathematical expression can be given as:\[F = k \frac{|q_1 q_2|}{r^2}\]where \( k \)is Coulomb's constant.- **Proportionality**: - Force increases with increasing magnitudes of the charges. - Force decreases as distance between charges increases.Coulomb's Law provides insights into how charges interact. It helps us understand the behavior of forces in electrostatic situations. For example, it explains why repulsive or attractive forces increase when charges are closer or larger.

Dielectric Constant

The dielectric constant is a measure of a material's ability to reduce the electric field within it. This concept is important when discussing how different mediums (like air and water) affect electrostatic forces.

- **Definition**: - Known as relative permittivity, it compares the permittivity of a substance with the permittivity of vacuum. - High dielectric constant implies strong reduction of electrostatic forces. When the medium between charges is air, the forces are more significant compared to when water is used. This is due to water's high dielectric constant. Water, having a greater ability to polarize and mitigate electric forces, results in a reduced effective force compared to air. This is why replacing air with water decreases the force between charges, illustrating the importance of the dielectric constant in electrostatics.

Electrostatic Force

Electrostatic force refers to the force between static electric charges. It is a non-contact force that can either attract or repel charges. Key aspects include: - **Nature of Force**: - Attractive between opposite charges. - Repulsive between like charges. Understanding electrostatic force includes appreciating how various factors, like the medium between charges, affect its strength. Replacing one medium with another, such as exchanging air for water between charges, results in changes to electrostatic force due to differing dielectric constants. Thus, the intervening medium plays a crucial role in electrostatic force, contradicting the misconception that it has negligible effects.