The drawing shows a graph of a set of equipotential surfaces...

The drawing shows a graph of a set of equipotential surfaces seen in cross section. Each is labeled according to its electric potential. A $+2.8 \times 10^{-7} \mathrm{C}$ point charge is placed at position $A .$ Find the work that is done on the point charge by the electric force when it is moved (a) from $A$ to $B,$ and (b) from $A$ to $C$.

Key Concepts

Electric Potential

Electric potential is a measure of the potential energy per unit charge at a point in an electric field. It is typically expressed in volts and represents the work needed per unit charge to move a test charge from a reference point (often infinity) to a specific point in the field without acceleration. Understanding this concept is essential for analyzing how potential energy varies with position in an electric field.

Equipotential Surfaces

Equipotential surfaces are geometric surfaces on which the electric potential is constant. They help visualize the electric field by showing regions where no work is done when moving a charge along the surface. This concept simplifies the analysis of electric fields by reducing complex 3-dimensional fields to easily interpretable 2-dimensional slices, and it is particularly useful when considering work done by or against the electric field.

Work Done by Electric Force

The work done by the electric force on a charge when it moves between two points in an electric field is determined by the potential difference between those points. Specifically, work is equal to the charge multiplied by the difference in electric potential (W = q?V). This concept applies the principle that for conservative forces, the work done depends only on the initial and final positions, not on the path taken, and it is crucial for solving problems involving energy changes in electric fields.

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