# Does the net force change over time for a proton that is moving through an electric and magnetic field?

Specifically perpendicular field. The electric field is going down and the proton is moving at a velocity through the magnetic field which is coming out of the page. So would the net force change over time? Why or why not? :/

Can someone please help me? I'm leaning towards that it doesn't because the different forces will only gain what is lost as the other energy (Ex. Potential into Kinetic)

### 1 Answer

- tiggerLv 79 years agoFavorite Answer
The net force on the proton will consist of 2 components:

1) An electric force Fe which is equal to E*qe where E the electric field, and qe is the charge on the proton. The direction of this force will be parallel to E.

2) A magnetic force Fm equal to qe*(B x v) = (H x v) *qe*u where B is the magnetic flux density, H is the magnetic field, and u is the permeability of the medium in which the particle moves. x signifies a vector cross product. The direction of this force changes since it accelerates the particle in a direction which is not parallel to the direction of v, and therefore the direction of v changes.

The constantly changing direction of Fm means that the net force (i.e the vector sum of Fm & Fe) will only be constant when Fm is zero - i.e. when the initial direction of v is parallel to B or H.

It is worth noting that your point about the conservation of energy leading to a constant force lacks a fully worked-through logical argument, and is in fact false. Consider a mass rotating in a vertical plane under the combined effect of gravity and centripetal force. Energy is conserved, but the net force on the mass is not constant either in magnitude or direction.

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