At a distance of 10 cm from the point charge, the field strength is 36 V / m. At what distance

At a distance of 10 cm from the point charge, the field strength is 36 V / m. At what distance from this charge is the voltage 900 V / m?

Given: r1 (distance from a point charge) = 10 cm (0.1 m); E1 (field strength at a given point) = 36 V / m; E2 (required field strength) = 900 V / m.

Since the field strength can be calculated by the formula: E = k * q / r2, and the value of the point charge is constant, then the equality will be true: q = E1 * r1 ^ 2 / k = E2 * r2 ^ 2 / k, whence r2 = √ (E1 * r1 ^ 2 / E2).

Calculation: r2 = √ (36 * 0.1 ^ 2/900) = 0.02 m (2 cm).

Answer: The field strength will be 900 V / m at a distance of 2 cm from the point charge.