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MIT Physics 8.02 - Electricity & Magnetism

SECTION : Electrostatics      

SUBJECT: Charge Moving in a Constant Field  

An example of the stresses transmitted by electric fields, and of the exchange of energy between fields and particles. An electric charge with charge q > 0 moves in a constant electric field. The charge is initially moving upward along the negative z-axis in a constant background field . The charge feels a constant downward force . The charge eventually comes to rest at the origin, and then moves back down the negative z-axis. This motion, and the fields that accompany it, are shown in the animation.

As the charge moves upward, it is apparent in the animation that the electric field lines are generally compressed above the charge and stretched below the charge. This field configuration enables the transmission of a downward force to the moving charge we can see as well as an upward force to the charges that produce the constant field, which we cannot see. The overall appearance of the upward motion of the charge through the electric field is that of a point being forced into a resisting medium, with stresses arising in that medium as a result of that encroachment.

Faraday would have described the downward force on the charge as follows: Surround the charge by an imaginary sphere centered on it. The field lines piercing the lower half of the sphere transmit a tension that is parallel to the field. This is a stress pulling downward on the charge from below. The field lines draped over the top of the imaginary sphere transmit a pressure perpendicular to themselves. This is a stress pushing down on the charge from above. The total effect of these stresses is a net downward force on the charge.




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