The force of repulsion between two people, each with the charge calculated in part (a), separated by a distance of 100 m, is approximately 0.0152 N.
The Earth has a net electric charge that generates a field near its surface, which is equal to 150 N/C directed towards the center of the planet. Let's address the questions:
(a) To overcome the weight of a human with the force exerted by the Earth's electric field, we need to calculate the electric force required.
The electric force (Fe) is given by the equation:
Fe = q * E
Where:
Fe is the electric force,
q is the charge, and
E is the electric field strength.
The weight (W) of the human is given by the equation:
W = m * g
Where:
W is the weight,
m is the mass of the human, and
g is the acceleration due to gravity.
Since the electric force and weight should be equal to achieve equilibrium, we have:
Fe = W
Therefore:
q * E = m * g
Rearranging the equation, we can solve for q:
q = (m * g) / E
Substituting the given values:
q = (60 kg * 9.8 m/s²) / 150 N/C
Calculating the value:
q ≈ 3.92 × 10⁻³ C
The charge required for a human to overcome their weight with the Earth's electric field is approximately 3.92 milli Coulombs. The sign of the charge would depend on whether the charge is positive or negative.
(b) To calculate the force of repulsion between two people with the charges calculated in part (a), we can use Coulomb's Law. Coulomb's Law states that the force of repulsion between two charges is given by:
F = k * (|q1| * |q2|) / r²
Where:
F is the force of repulsion,
k is the electrostatic constant (9 × 10^9 N m²/C²),
q1 and q2 are the charges, and
r is the distance between the charges.
Substituting the values:
F = (9 × 10^9 N m²/C²) * (3.92 × 10⁻³ C)² / (100 m)²
Calculating the value:
F ≈ 1.52 × 10⁻² N
The force of repulsion between two people, each with the charge calculated in part (a), separated by a distance of 100 m, is approximately 0.0152 N.
As for the feasibility of using the Earth's electric field as a means of flying, it is not practical. The magnitude of the electric field near the Earth's surface is relatively weak, and the forces involved are insufficient to counteract the weight of a human. Additionally, the charges required for such an effect would be extremely large and potentially dangerous. The Earth's electric field cannot be effectively used as a medium for flying.