Problem 81 - Master Resource Book in JEE Main Physics

Question

A positively charged particle is released from rest in an uniform electric field. The electric potential energy of the charge [NCERT Exemplar] (a) remains a constant because the electric field is uniform (b) increases because the charge moves along the electric field (c) decreases because the charge moves along the electric field (d) decreases because the charge moves opposite to the electric field

Step-by-Step Solution

Answer

(c) The electric potential energy decreases because the charge moves along the electric field.

Step 1: Understanding Electric Potential Energy

Electric potential energy is the energy a charged particle has due to its position within an electric field. It is given by the formula \[ U = qV \]where \( q \) is the charge, and \( V \) is the electric potential at the charge's location.

Step 2: Analyzing the Movement and Charge Characteristics

Since the particle is positively charged and released from rest, it will move in the direction of the electric field. The electric field naturally pushes positive charges along its direction, reducing the potential energy as the charge moves.

Step 3: Electric Potential Energy Change in Uniform Field

When a positively charged particle moves along the direction of an electric field, it moves from a region of higher potential to lower potential. Hence, the electric potential energy decreases as it moves in this direction.

Key Concepts

Uniform Electric Field

An **uniform electric field** is a region where the electric force experienced by charges is consistent in magnitude and has the same direction throughout. This is crucial when understanding how a charged particle behaves. In such a field, the field lines are parallel and equally spaced, indicating no change in the field's strength.
One key feature of a uniform electric field is that it exerts the same force across the entire space. Concepts like electric potential energy are simplified because the change in potential energy is the same regardless of the path taken by a charge.
When considering movement within a uniform electric field, the potential difference, which is the work done per unit charge to move a charge from one point to another, is what influences the kinetic and potential energies of charged particles.

Charged Particles

**Charged particles** are objects with an imbalance in the number of protons and electrons, giving them a net electric charge. These particles can be either positive or negative charges, influencing how they interact with electric fields.
For a positively charged particle, such as a proton, it will be attracted towards regions of lower electric potential in an electric field. The movement of charged particles in response to an electric field is fundamental in many electrical phenomena.
A charge's potential energy is related to its position in the field, as described by \[ U = qV \] Where \( U \) is the potential energy, \( q \) is the charge, and \( V \) is the electric potential. When released, the acceleration of a particle will occur in the direction of force applied by the field, affecting both its potential and kinetic energies.

Electric Field Direction

The **electric field direction** is fundamentally important for understanding the motion of charged particles. The direction of an electric field is defined as the direction a positive test charge would move if placed in the field. This aligns with how the field affects positively charged particles.
In practical scenarios, a positively charged particle released in a uniform electric field will accelerate in the direction of the field lines. This scenario causes the potential energy to decrease as kinetic energy increases, confirming the transformation of energy types.
For negative charges, the effect is opposite; they move against the direction of the field lines, which can result in an increase in potential energy if free to move.