Understanding Work Done in Moving Charge

The question asks us to calculate the work done when a specific amount of electric charge is moved across two points with a known potential difference. This is a fundamental concept in electrostatics.

What is Potential Difference?

Potential difference (V) between two points is defined as the work done per unit charge to move a positive charge from one point to the other. Mathematically, it is expressed as:

\(V = \frac{W}{Q}\)

Where:

• \(V\) is the potential difference
• \(W\) is the work done
• \(Q\) is the electric charge moved

Calculating Work Done from Potential Difference

From the definition of potential difference, we can rearrange the formula to find the work done (\(W\)):

\(W = V \times Q\)

This formula tells us that the work done in moving a charge is the product of the potential difference and the magnitude of the charge.

Applying the Formula to the Given Problem

We are given the following values:

• Magnitude of charge, \(Q\) = 2 Coulombs (C)
• Potential difference, \(V\) = 12 Volts (V)

We need to find the work done, \(W\).

Using the formula \(W = V \times Q\), we substitute the given values:

\(W = 12 \, \text{V} \times 2 \, \text{C}\)

Now, we perform the multiplication:

\(W = 24 \, \text{Joule}\)

The unit of work done is Joules (J).

Conclusion on Work Done Calculation

Based on our calculation, the work done in moving 2 Coulombs of charge across two points having a potential difference of 12 V is 24 Joules.

Revision Table: Key Concepts

Additional Information on Work, Charge, and Potential

Understanding the relationship between work, charge, and potential difference is crucial in electricity. Here are some related points:

• Potential difference is often referred to as voltage.
• Moving a positive charge from a lower potential point to a higher potential point requires work to be done by an external agent.
• If a positive charge moves from a higher potential point to a lower potential point, the electric field does work on the charge, and its potential energy decreases.
• 1 Volt is defined as 1 Joule of work done per Coulomb of charge moved (\(1 \, \text{V} = 1 \, \text{J/C}\)). This aligns perfectly with the formula \(W = V \times Q\).

This example demonstrates a direct application of the definition of potential difference to calculate the energy transferred (work done) in an electrical system.