Magnetic Field Of Two Moving Charges

Instructions

This applet is designed to allow you to explore the concept of the superposition of magnetic fields from two moving charges (see page 436 of EMI for the expression of the magnetic field of a single moving charge). Both charges are positively charged, and are in the plane of the screen moving perpendicular to that plane. The particle on the left is always moving out of the page. The particle on the right is initally moving into the page. You can reverse the direction of its motion by pressing the "Reverse Direction of Velocity" button.

To change the ratio of the speeds of the particles (initially set to one), increase that ratio by hitting the corresponding button on the lower right. To move either change, click and drag on that charge.

The configuration of the total magnetic field is shown by a vector field diagram: the small arrows point in the direction of the local field with a color that shows the strength of that field (red strongest, fading away to invisible). You can also see the field lines by clicking in any space away from the two charges or the tail of the blue arrow.

You can see how this vector field arises by looking at the red, black and blue vectors. The red and black vectors show the magnetic fields due to each charge (the tail of the red (black) vector is connected by a red (black) line to the particle which produces it on the right (left). The blue vector is the vector sum of those two individual magnetic fields, and shows the total magnetic field. Click and drag in the vicinity of the tail of the blue vector and you can explore the magnetic field of two moving charges and see how it arises from adding up the two individual fields by vector addition.

To get this applet to run faster on a slow computer, increase the "Speed" by upping that parameter with the button on the lower left.