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When we talk about work done by an electric force, we are discussing the energy required to move a charge from one point to another in the presence of an electric field. Imagine pushing a shopping cart uphill; the work done is the effort it takes to move it. Similarly, in the world of charges, work is needed to move these tiny particles against the forces within an electric field.

To calculate the work done by an electric force, we use the formula:

• \( W = q \cdot (V_A - V_B) \)

- Here, \( W \) represents work in joules (J).- \( q \) is the charge, which is what we're solving for.- \( V_A - V_B \) is the electric potential difference between points A and B.

Knowing how much work is done is crucial because it helps us determine the amount of energy used or needed in processes involving charges, such as in circuits or electronic devices.

The electric potential difference, often dubbed voltage, is a measure of how much potential energy a charge has at one point compared to another. Think of it like the difference in height between two points on a hill; the higher you are, the more potential energy you have.

In terms of electric charges:

• The potential difference \( V_A - V_B \) tells us how much work is needed to move a unit of charge from point B to point A.

- A higher potential difference means more work is needed to move the charge, similar to climbing a steeper hill.

In the context of the problem, the potential difference is given as 50.0 V. This tells us that a potential energy change of 50.0 joules would occur per coulomb of charge moving between the two points. Understanding potential difference helps us grasp how and why charges move, which is fundamental in technologies like batteries and power supplies.

Electrostatics is the study of forces between charges, and it relies on key formulas to describe these interactions. These formulas help us predict how charges behave in an electric field.

Here are some core formulas in electrostatics:

• **Coulomb's Law:** \( F = k \cdot \frac{|q_1 \cdot q_2|}{r^2} \)
  This formula calculates the force between two charges, where \( F \) is the force, \( k \) is the electrostatic constant, \( q_1 \) and \( q_2 \) are the charges, and \( r \) is the distance between them.
• **Electric Field:** \( E = \frac{F}{q} = k \cdot \frac{|q|}{r^2} \)
  The electric field \( E \) represents the force per unit charge exerted on a small positive charge in the field.
• **Work Done by Electric Force:** \( W = q \cdot (V_A - V_B) \)
  This is the formula used in the given problem, linking work, charge, and potential difference.

Understanding these formulas is essential as they form the backbone of electrostatics theory. They provide insights into interactions between charges, how to calculate forces and fields, and lead us to solve practical problems in electric circuits and beyond.