An infinite charged plane has a surface charge density of 9 * 10 ^ {- 8} C / m ^ {2}.

| August 17, 2021 | education

An infinite charged plane has a surface charge density of 9 * 10 ^ {- 8} C / m ^ {2}. Above it is an aluminum ball with a charge of 3.68 * 10 ^ {- 7} Cl. What mass should the ball have so that it does not fall?

To find the required mass of the specified aluminum ball, we use the equality: Ft = Fe; m * g = q * E and m = q * E / g = q * (Ϭ / 2ε0) / g = q * Ϭ / (2ε0 * g).

Constants and variables: q – charge of the specified aluminum ball (q = 3.68 * 10-7 C); Ϭ – surface charge density (Ϭ = 9 * 10-8 C / m2); ε0 – electrical constant (ε0 = 8.854 * 10-12 F / m); g – acceleration due to gravity (g = 9.81 m / s2).

Calculation: m = q * Ϭ / (2ε0 * g) = 3.68 * 10-7 * 9 * 10-8 / (2 * 8.854 * 10-12 * 9.81) = 1.9 * 10-4 kg = 0.19 g.

Answer: The mass of the specified aluminum ball should be 0.19 g.



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