Question

The figure represents the variation of the electric potential \( V \) at a point in a region of space as a function of its position along the x-axis. A charged particle will experience the maximum force at:

• A. P
• B. Q
• C. R
• D. S

Hint:

In \( V \) vs \( x \) graphs: - Electric field = negative slope of the graph. - Maximum force occurs where the graph is steepest (largest slope magnitude).

Answer 1

The Correct Option is D

The problem involves finding the point where a charged particle experiences the maximum force based on the variation of electric potential along the x-axis.

The electric force experienced by a charged particle is related to the electric potential (V) by the electric field (E). The electric field is the negative gradient of the electric potential, represented mathematically as:

\(E = -\frac{dV}{dx}\)

The magnitude of the electric force (F) on a charged particle with charge \( q \) is given by:

\(F = qE\)

Therefore, the point at which the electric field is steepest (i.e., where the change in electric potential is steepest) corresponds to the point where the particle will experience the maximum force.

To determine the maximum force location from the provided graph, observe where the slope of \( V \) versus \( x \) is steepest. The slope at points \(P, Q, R,\) and \(S\) are examined:

1. At point \(P\), the slope is not as steep.
2. At point \(Q\), the slope decreases slightly.
3. At point \(R\), the slope is moderate.
4. At point \(S\), the slope is steepest among the considered points.

Therefore, the maximum change in potential, and hence maximum magnitude of electric field, occurs at point \(S\). Consequently, the charged particle will experience the maximum force at this point.

Correct Answer: \(S\)