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Coulomb's Law is fundamental for understanding the interactions between electric charges. It describes the force between two point charges. The formula is:

• \( F = \frac{k|q_1 q_2|}{r^2} \)

This means the force \( F \) is proportional to the product of the magnitudes of the charges, \( q_1 \) and \( q_2 \), inversely proportional to the square of the distance \( r \) between them, and dependent on the constant \( k \), known as Coulomb's constant (\(8.99 \times 10^9 \text{ N }\cdot\text{m}^2/\text{C}^2\)).
The force can be attractive or repulsive, depending on the signs of the charges. Like charges repel, while opposite charges attract. Understanding this law is crucial for solving problems related to electric forces, such as how two people would repel each other if they both had the same charge.

Gravitational force is the force of attraction between two masses. On Earth, this force gives us our weight. The weight of an object is calculated by multiplying its mass by the acceleration due to gravity, usually denoted \(g\).
For a person weighing 60 kg on Earth, the gravitational force is:

• \( F_g = mg = 60 \times 9.8 = 588 \text{ N} \)

This formula highlights the direct relationship between mass and gravitational force.
While solving physics problems, understanding gravitational force is essential, especially when considering other forces like electric force that might oppose or counteract gravitational pull.

Electric force is the force exerted by an electric field on a charge. The magnitude of this force is given by the formula:

• \( F_e = qE \)

Where \( F_e \) is the electric force, \( q \) is the charge, and \( E \) is the electric field.
In this exercise, the electric field from Earth is \(150 \text{ N/C}\). For a person to counteract their weight using this electric field, the electric force must equal their gravitational force.
Hence:

• \( qE = mg \)

This balance of forces allows the calculation of the charge required to overcome gravitational force, highlighting the interplay between different physical forces.

Calculating charge is crucial for determining how much charge is needed to achieve a certain electric force. From the given exercise, to overcome the gravitational force with an electric force, we compute:

• \( q = \frac{mg}{E} = \frac{588}{150} \approx 3.92 \text{ C} \)

This result shows the amount of charge required for a 60 kg person to levitate in Earth's electric field.
It's also important to consider the sign of the charge. Because the Earth's electric field is directed inward, a positive charge would produce an upward force, essential for levitation.
However, this calculated charge is unrealistically high for everyday use, demonstrating that using such a method for flight is not feasible with current technology.