Magnetic Field From a Moving Point Charge

The field from a point charge whose velocity is small compared to the speed of light can be found by adapting the Biot-Savart law. Notice that Idl can be written in terms of the velocity by shifting the dt from the current to the dl.

Put this into the Biot-Savart law and integrate it for the dq assuming all pieces of the charge have the same speed and distance r (for a point charge this is always true).

What does this B-Field look like? To explore its properties we are going to use the SilverHammer program.

Double-click the icon for SilverHammer. Choose the Charge Tool and drag a charge. Choose the Velocity Tool and give it a velocity. Choose "Use Magnetic Field" from the "Fields" Menu. Go to the graph window and draw a color density graph.

How can you tell from the graph what line the particle is moving along?

Check Answer.

What shape does the B-field have, that is, how does one of the contour lines depend on the angle with the axis of motion?

First work out the cross product and record your result in your journal.

Check Answer.


Go to Point Charge Field lines.