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In physics, the concept of work is closely tied to the idea of energy transfer. When it comes to electric forces, work is the energy required to move a charge from one point to another in an electric field. The work done by electric force can also help us understand how energy is distributed and used in electrical systems.
When a charge is moved in an electric field, electric force does work on the charge. This work is calculated as the product of the electric charge, the distance moved in the field, and the cosine of the angle between the force and the direction of movement. However, in the case of potential difference, the equation simplifies to the one given in the problem:

• Work, \( W \), is measured in joules (J).
• Charge, \( q \), is measured in coulombs (C).
• Potential difference, \( V_A - V_B \), is in volts (V).

The important takeaway is that the work done by electric forces directly relates to how much energy is required to move electric charges within an electric field.

The relationship between work, charge, and potential difference is a fundamental concept in electromagnetism. This relationship is expressed mathematically as \[ W = q \times (V_A - V_B) \] where:

• \( W \) is the work done.
• \( q \) is the electric charge being moved.
• \( V_A - V_B \) is the potential difference or voltage change between two points.

This equation allows us to determine any one of the variables if the others are known. In essence, it demonstrates that the work done to move a charge in an electric field is proportional to both the size of the charge and the potential difference it moves across.
This relationship helps illustrate how electric fields can exert forces and do work, providing energy to move charges. Understanding this interaction is crucial for solving problems related to electric circuits and various electronic devices.

To calculate the charge when work done and potential difference are known, we rearrange the formula for electric work: \[ q = \frac{W}{V_A - V_B} \]Let's walk through this calculation:1. **Identify the given values**: The problem provides us with the work done \( W = 2.70 \times 10^{-3} \) Joules and the potential difference \( V_A - V_B = 50.0 \) Volts.2. **Substitute these values into the formula**: \[ q = \frac{2.70 \times 10^{-3}}{50.0} \]3. **Perform the division to obtain the charge**: \[ q = 5.40 \times 10^{-5} \] Coulombs.
By following this method, we determine how much electric charge was moved, given the energy expended and the voltage difference. This calculation is particularly useful in designing electrical systems and measures how charges flow in different conditions.