Levitation by electric field

Electricity and Magnetism Level 2

A charged particle is placed in a uniform vertical electric field which varies with time as E 0 sin ⁡ ( ω t ) E_0 \sin (\omega t) .

Is it possible to levitate the particle using this field?

Only if E 0 E_0 is large Only if ω \omega is large No, it's not possible

Pranshu Gaba by Pranshu Gaba , 22, India

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1 solution

Tom Engelsman
Sep 10, 2018

Let the charged particle in question have charge q q and mass m m . In order for it to levitate in the presence of the electric field, its weight must equal the force induced by this field. That is:

m g = F = q E mg = F = qE ;

or m g q = E 0 s i n ( ω t ) \frac{mg}{q} = E_{0}sin(\omega t) .

The result is a non-constant sinusoidal function equaling a constant as time t t varies.....CONTRADICTION.

2 Helpful 1 Interesting 1 Brilliant 0 Confused

Even if we relax the requirement and say that "levitate" means that the displacement from the initial location is finitely bounded as time goes to infinity, it still can't levitate.

Steven Chase - 2 years, 9 months ago

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