Problem 123 - 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 The electric field and hence electric field lines are everywhere at right angle to an equipotential surface. Reason Equipotential surfaces are closer together where the electric field is stronger and farther apart where the field is weaker.

Step-by-Step Solution

Answer

(b) Both Assertion and Reason are true but Reason is not the correct explanation of the Assertion.

Step 1: Understand the Assertion

The assertion states that the electric field and electric field lines are perpendicular (at right angles) to an equipotential surface. This is a fundamental property of electric fields; the lines of force must be perpendicular to surfaces of constant potential because no work is done when moving a charge on an equipotential surface.

Step 2: Analyze the Reason

The reason states that equipotential surfaces are closer together where the electric field is stronger and farther apart where the field is weaker. This is also a true statement reflecting how the potential difference between surfaces changes in stronger versus weaker fields; in stronger fields, potential changes more quickly, resulting in closer surfaces.

Step 3: Assess the Logical Connection

While both statements independently describe true attributes concerning electric fields and equipotential surfaces, the reason provided is not a direct explanation of why electric field lines are perpendicular to equipotential surfaces. The reason relates more to the intensity of the field rather than the orientation of the field lines.

Step 4: Determine the Correct Answer

Since both the assertion and the reason are true, but the reason does not directly explain why the assertion is true, the correct answer is (b).

Key Concepts

Electric Field

Imagine the electric field as an invisible force field that surrounds charged particles, much like how gravity surrounds planets. It is a vector field, which means it has both magnitude and direction at each point in space. The strength of the electric field is determined by how charged particles influence each other from a distance.

The direction of the electric field is crucial. It points away from positive charges and towards negative charges. This directionality helps in visualizing how a force acts on a positive test charge placed in the field. To calculate the electric field at a point, we use the formula:

• The electric field, \(E\), is given by \(E = \frac{F}{q}\)
• Where \(F\) represents the force experienced by a test charge \(q\).

A key property is that the electric field exerts no work on a charge moving along an equipotential surface, because the potential energy remains constant.

Electric fields help in understanding how electric forces are propagated through space. They are fundamental in numerous applications, such as in electric circuits, capacitors, and more.

Equipotential Surfaces

Equipotential surfaces are fascinating concepts in electrostatics. These are imaginary surfaces where every point on the surface has the same electric potential. Think of them as contour lines on a topographic map where height is constant.

What's special about equipotential surfaces is that they illustrate regions in an electric field where a charge can move without doing any work. This is because the electric potential does not change along these surfaces. As a result, moving a charge across an equipotential surface neither requires nor releases any energy.

Equipotential surfaces reflect the strength of the electric field. Where these surfaces are closer together, the electric field is stronger, illustrating that potential changes rapidly. Conversely, when they are spaced further apart, the electric field is weaker and potential changes slowly. This principle is crucial for visualizing the intensity of electric fields and helps in understanding the distribution of electric potential in space.

Electric Field Lines

Electric field lines provide a visual representation of the electric field. Think of them as arrows showing the direction that a positive test charge would move if placed in the field. These lines emerge from positive charges and terminate at negative charges.

A notable property of electric field lines is that they are always perpendicular to equipotential surfaces. This perpendicularity ensures that no work is done by or against the electric field when a test charge moves along an equipotential surface. Thus, electric field lines help us understand not only the direction of the force exerted by the field but also its interaction with potential surfaces.

The density of these lines indicates the strength of the electric field: more lines mean a stronger field. Additionally, electric field lines never cross each other. If they did, it would mean there are two different directions for the electric field at a single point, which is not possible.

Understanding electric field lines is essential in visualizing electric phenomena, from the operation of capacitors to the behavior of charges in electric fields.