At what distance along the central axis of a uniformly charged plastic disk of radius r = 0.525 m is the magnitude of the electric field equal to 1/5 times the magnitude of the field at the center of the surface of the disk?

The general formula for the strength of magnetic field is written below:

E = kQ/d²,
where k is the Coulomb's constant
Q is the charge of the object
d is the distance

The ratio of the magnetic fields should be 1/5:

E₁/E₂ = 1/5
kQ/d₁² ÷ kQ/d₂² = 1/5
The k and Q will be cancelled out because only the distance is varied, the charge does not change. The equation becomes

1/d₁² ÷ 1/d₂² = 1/5
Substitute d₁ = 0.525 m
1/(0.525 m)² ÷ 1/d₂² = 1/5
Solving for d₂,
d₂ = 0.235 m

The distance is 0.235 m along the central axis.

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