An electromagnetic standing wave in air of frequency 750 MHz is set up between two conducting planes 80.0 cm apart. At how many positions between the planes could a point charge be placed at rest so that it would remain at rest?

The positions the point charge will be placed at rest and still remain at rest are 20 cm, 40 cm, and 60 cm between the ends.

Explanation:

Given;

distance between the conducting planes, d = 80 cm

frequency of the electromagnetic wave, f = 750 MHz

speed of light, c = 3 x 10⁸ m/s²

Determine the wavelength

λ = C/f

where;

λ is the wavelength

C is the speed of light

f is the frequency

λ = C/f

λ = (3 x 10⁸) / (750 x 10⁶)

λ = 0.4 m = 40 cm

One complete cycle = one wavelength = 40 cm

half of the wavelength ( λ / 2) = 20 cm

one wavelength + half wavelength (3λ / 2) = 60 cm

The positions of the wave at zero amplitude (between 0 and 80 cm) = 20 cm, 40 cm, 60 cm

Thus, the positions the point charge will be placed at rest and still remain at rest are 20 cm, 40 cm, and 60 cm between the ends.

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