Problem 119 - 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 A point charge is brought an electric field. The field at a nearby point will be increase. Whatever the nature of charge. Reason The electric field is independent of the nature of charge.

Step-by-Step Solution

Answer

(c) Assertion is true but Reason is false.

Step 1: Identifying the Assertion

The assertion given is that when a point charge is brought near an electric field, the field at a nearby point will increase regardless of the charge's nature.

Step 2: Understanding the Reason

The reason states that the electric field is independent of the nature of the charge.

Step 3: Analyzing the Assertion

The assertion suggests that introducing a point charge in the vicinity of an existing electric field will lead to an increase in the field strength at a nearby point. This assertion is partially correct, as bringing a charge into a field does modify the field, but this effect depends on additional factors like the charge's sign and magnitude.

Step 4: Analyzing the Reason

The reason claims that the electric field is independent of the nature of the charge. This is false because the electric field produced by a charge is directly related to the magnitude and nature (sign) of the charge. Therefore, the reason provided is incorrect.

Step 5: Evaluating the Assertion and Reason

Since the assertion implies that the presence of any charge increases the field without considering the charge sign or magnitude, and the reason incorrectly states that the field is independent of the charge's nature, both the assertion and reason are flawed. However, if we consider them separately, the assertion can hold under specific conditions, but the reason is clearly false.

Step 6: Choosing the Correct Option

Both the assertion and reason are not entirely accurate, but the assertion can be considered true under limited circumstances, while the reason is false. Therefore, the correct option to choose is (c), where the assertion is true but the reason is false.

Key Concepts

Electric Field

An electric field is a region around a charged object where other charges experience a force. It emanates from positive charges and converges towards negative charges. The lines representing an electric field show the direction a positive test charge would move. These field lines never cross and indicate the strength and direction of the field. The density of these lines signifies the field's strength; a higher density means a stronger field. Understanding electric fields is crucial in physics, as they help visualize how forces are transmitted through space due to charges.
Measuring the electric field depends on the amount of force experienced per unit charge, measured in newtons per coulomb (N/C). This foundational concept helps in designing electronic circuits and understanding natural phenomena such as lightning.

Point Charge

A point charge is an idealized concept of a charged particle with negligible size, which simplifies the calculation of electric fields and forces. In mathematical terms, a point charge is considered as a source of an electric field with its entire charge concentrated at a single point. This assumption allows us to easily apply Coulomb's law to find the electric field strength due to a point charge.
The formula for the electric field \( E \) generated by a point charge \( q \) is given by:

• \( E = \frac{k \cdot q}{r^2} \)

Here, \( k \) is Coulomb's constant, approximately equal to \( 8.99 \, \times \, 10^9 \, \text{N} \, \text{m}^2/\text{C}^2 \), and \( r \) is the distance from the charge.
Despite its simplicity, this model is highly effective for solving problems in electrostatics, particularly in understanding the behavior of charges when approaching or interacting at significant distances.

Nature of Charge

The nature of charge refers to its fundamental property: either positive or negative. Charge is a crucial concept, essential for understanding how objects interact electrically. It determines how charges exert forces on each other, as like charges repel and opposite charges attract.
This nature is key to comprehending electric interactions. Each charge's behavior can significantly affect the surrounding electric field, modifying field lines based on its sign. The charge magnitude also influences the electric field strength, making every charge unique in its effect. Understanding the nature of charge lays the groundwork for predicting and explaining various electrical phenomena, from simple static electricity to complex circuitry.
Remember, any change in the charge's polarity or magnitude can lead to different electric interactions, significantly impacting the characteristics of electric fields.

Electric Field Strength

Electric field strength is a measure of the force exerted per unit charge at any point within the field. It tells us how strong the electric field is at a particular location and is determined by the charge causing the field and the distance from this charge. This strength is a vector quantity, having both magnitude and direction, which makes it essential for understanding the influence of electric fields on charges.
The formula is expressed as \( E = \frac{F}{q_0} \), where \( F \) is the force experienced by a test charge \( q_0 \). In the case of a point charge, the electric field strength varies inversely with the square of the distance from the charge, emphasizing its rapid decrease as the distance increases.

• A stronger electric field means a larger force on a test charge.
• Its magnitude can change depending on the charge and distance.

Understanding electric field strength is crucial in predicting how and where charges will move, helping us harness electricity in various applications.