Problem 154 - A Complete Resource Book in Physics for JEE Main

Question

On moving a charge of \(20 \mathrm{C}\) by \(2 \mathrm{~cm}, 2 \mathrm{~J}\) of work is done. The potential difference between the points (A) \(0.1 \mathrm{~V}\) (B) \(8 \mathrm{~V}\) (C) \(2 \mathrm{~V}\) (D) \(0.5 \mathrm{~V}\)

Step-by-Step Solution

Answer

The potential difference between the points is \(0.1 \, \text{V}\). Therefore, the correct answer is (A) \(0.1 \, \text{V}\).

Step 1: Write down the given information

We are given: - Charge, Q = 20 C - Work done, W = 2 J

Step 2: Calculate the potential difference

To find the potential difference, we can use the formula: \( V = \frac{W}{Q} \) Now, plug the values of W and Q into the formula: \( V = \frac{2 \, \text{J}}{20 \, \text{C}} \)

Step 3: Solve for V

Simplify the equation to find V: \( V = \frac{1}{10} \, \text{V} \) \( V = 0.1 \, \text{V} \) The potential difference between the points is \(0.1 \, \text{V}\). Therefore, the correct answer is: (A) \(0.1 \, \text{V}\)

Key Concepts

Work Done on Charge

The concept of work done on a charge is an important aspect of electric fields and potential energy. When we talk about work done, we are essentially considering the energy required to move a charge within an electric field. This energy transfer plays a crucial role in how we understand electricity.

To illustrate this with our problem, imagine you are pushing a pebble up a hill. It takes effort, and similarly, moving a charge of 20 Coulombs (C) involves work, 2 Joules (J) in this case. The amount of work done depends not only on the charge being moved but also on the strength of the electric field.

Key points about work done on a charge:

• Measured in Joules (J).
• Work is done when a charge moves through a potential difference.
• Depends on both the amount of charge and the potential difference.

Grasping the concept of work done helps us in calculating potential difference and understanding energy conversion in electric circuits.

Electric Potential

Electric potential or voltage is a measure of potential energy per unit charge at a point in an electric field. Think of it like a pressure difference or height difference, indicative of potential to do work. Higher electric potential means more capability to move charge.

In our example, the charge is moved between two points with a specific amount of work done, giving a clue to the potential difference.

Some characteristics of electric potential include:

• Measured in Volts (V).
• Represents energy per unit charge.
• High potential means greater ability to do work on a charge.

By understanding electric potential, we can effectively interpret how energy is stored and transferred within an electric field, translating directly into calculations of potential difference as shown in the given problem.

Formula for Potential Difference

The formula for potential difference is a fundamental equation in electromagnetism. This formula allows us to determine the potential difference across two points in an electric field by utilizing the work done and the charge involved. In simple terms, it tells us how much potential energy is converted into electrical energy, divided by the charge.

The formula for potential difference (V) is:\[ V = \frac{W}{Q} \]where:

• \(V\) is the potential difference in volts (V)
• \(W\) is the work done in joules (J)
• \(Q\) is the charge in coulombs (C)

Using this formula, we observed in our exercise how a 2 Joule work done on a 20 Coulomb charge results in a potential difference of 0.1 volts.

This formula provides an essential tool for engineers and physicists to analyze electrical circuits and predict their behavior efficiently.