The drawing shows the potential at five points on a set of...

The drawing shows the potential at five points on a set of axes. Each of the four outer points is $6.0 \times 10^{-3} \mathrm{~m}$ from the point at the origin. From the data shown, find the magnitude and direction of the electric field in the vicinity of the origin.

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Key Concepts

Relationship between Electric Potential and Electric Field

This fundamental concept connects the scalar electric potential to the vector electric field through the relation E = -?V. It provides a method to determine the magnitude and direction of the electric field by analyzing how the electric potential changes spatially.

Gradient (and Finite Difference Approximation)

The gradient is an operator that measures the rate and direction of change in a scalar field. In the context of electric fields, it is used to calculate the electric field from variations in electric potential. When using experimental or discrete data points, a finite difference approximation is often employed to estimate this gradient.

Electric Potential

This is a scalar quantity that represents the electric potential energy per unit charge at a specific point in space. It provides a measure of the work done in bringing a test charge from infinity to that point without any acceleration, and is usually expressed in volts.

Electric Field

The electric field is a vector quantity that quantifies the force per unit charge a test charge would experience at a given point. It is defined as the negative gradient of the electric potential, indicating that the field points in the direction of the steepest decrease in potential.

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