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TEAL Electricity & Magnetism

SECTION : Force on Moving Charges   

SUBJECT: Charge Moving in a Magnetic Field (Front)  
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The animation shows a charge moving toward a region where the magnetic field is vertically upward. When the charge enters the region where the external magnetic field is non-zero, it is deflected in a direction perpendicular to that field and to its velocity as it enters the field. This causes the charge to move in an arc that is a segment of a circle, until the charge exits the region where the external magnetic field in non-zero. We show in the animation the total magnetic field-that is the magnetic field of the moving charge in addition to that of the external magnetic field. The bulging of the total field on the side opposite the direction in which the particle is pushed is due to the build up in magnetic pressure on that side. It is this pressure that causes the charge to move in the arc of a circle.

The moving charge in the animation changes its direction of motion by ninety degrees over the course of the animation. How do we conserve momentum in this process? Momentum is conserved because momentum is transmitted from the moving charge to the currents that are generating the constant external field. This is plausible given the field configuration shown in the animation. The magnetic field stress, which pushes the moving charge sideways, is accompanied by a tension pulling the current source in the opposite direction.

To see this, look closely at the field stresses where the external field lines enter the region where the currents that produce them are hidden, and remember that the magnetic field acts as if it were exerting a tension parallel to itself. The momentum loss by the moving charge is transmitted to the hidden currents producing the constant field in this manner.



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