A Charge q is displaced from point P1 to P2. FInd the work done

To determine the work done when a charge \( q \) is displaced from point \( P_1 \) to point \( P_2 \), we need to consider the electric field in which the charge is moving. The work done on a charge in an electric field is calculated using the formula:

Understanding Work in Electric Fields

The work \( W \) done by an electric field when moving a charge is given by:

W = q * ΔV

Here, \( ΔV \) represents the change in electric potential (voltage) between the two points \( P_1 \) and \( P_2 \). This formula indicates that the work done is directly proportional to the charge and the potential difference it experiences during its displacement.

Breaking Down the Components

• Charge (q): This is the amount of electric charge being moved, measured in coulombs (C).
• Electric Potential Difference (ΔV): This is the difference in electric potential between the two points, calculated as \( V(P_2) - V(P_1) \).

Calculating the Work Done

To find the work done, follow these steps:

1. Identify the electric potentials at points \( P_1 \) and \( P_2 \). Let's say \( V(P_1) = V_1 \) and \( V(P_2) = V_2 \).
2. Calculate the potential difference: \( ΔV = V_2 - V_1 \).
3. Substitute the values into the work formula: \( W = q * ΔV \).

Example Calculation

Imagine a scenario where a charge \( q = 2 \, \text{C} \) is moved from point \( P_1 \) where the electric potential \( V_1 = 5 \, \text{V} \) to point \( P_2 \) where \( V_2 = 10 \, \text{V} \).

First, calculate the potential difference:

ΔV = \( V_2 - V_1 = 10 \, \text{V} - 5 \, \text{V} = 5 \, \text{V} \)

Now, substitute into the work formula:

W = \( q * ΔV = 2 \, \text{C} * 5 \, \text{V} = 10 \, \text{J} \)

Thus, the work done in moving the charge from \( P_1 \) to \( P_2 \) is \( 10 \, \text{J} \).

Key Points to Remember

• The work done is dependent on both the charge and the potential difference.
• In a uniform electric field, the work can also be calculated using the force and displacement, but the potential difference approach is often simpler.
• Work done can be positive or negative depending on the direction of the charge movement relative to the electric field.

By understanding these concepts, you can effectively calculate the work done on a charge as it moves through an electric field. If you have any further questions or need clarification on any part of this process, feel free to ask!