When a charge is placed in an alternating electric field it will oscillate according to the alternating force on it. If the time spent in each field direction is equal it should return to the same position after one cycle. This assumption is only true under the condition that the electric field is perfectly homogeneous and so there is no change of electric field strength as a function of distance. If the field is inhomogeneous, it will clearly have a gradient of field strength over the distance the charge oscillates. While the charge performs its half cycle within the stronger field it will experience greater returning force than the half of the cycle in the weaker section of field. This leads to, over one complete oscillation, an average force transporting the particle from strong to weak field. This is called the ponderomotive force and has the mathematical form:

Where **e **and **m** are the charge and mass of the particle, **ω **is the angular frequency of the field’s oscillations and the final term is the gradient of the electric field strength, **E**, squared (if **E **is small enough the action of the magnetic field can be ignored).

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