Trajectory of a Test Charge in an Electric Field

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This Demonstration computes the path a test charge would take in the electric field of two fixed-point charges. Blue and red indicate a negative and positive charge, respectively. Use the controls "", "" and "test charge" to change the magnitudes of the charges. Drag the locators to change the positions of the charges. The path is shown as a black curve.

Contributed by: Aidan Zhang (February 2020)
Open content licensed under CC BY-NC-SA



The test charge follows a path that minimizes the work done by the force field. Given the initial position of the test charge, the Manipulate generates this path by finding the direction of maximum work done at each point and extending the path by 0.1 units in the same direction.

Since creating the path is a recursive process that ends given a distance threshold, setting all the charges to have the same sign repels the charges to infinity. This significantly slows down the Manipulate. For faster results, make sure the test charge has an opposite charge from at least one of the fixed charges.

This was a project for Advanced Topics in Mathematics II, 2019–2020, Torrey Pines High School, San Diego, CA.

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