Question

how does the electrical force relate to the charge of an object?
○ it is inversely proportional to the square of the charge.
○ it is directly proportional to the square of the charge.
○ it is inversely proportional to the charge.
○ it is directly proportional to the charge.

Explanation:

To determine the relationship between electrical force and the charge of an object, we refer to Coulomb's Law, which is given by \( F = k\frac{q_1q_2}{r^2} \), where \( F \) is the electrical force, \( k \) is a constant, \( q_1 \) and \( q_2 \) are the charges of the two objects, and \( r \) is the distance between them. From this formula, we can see that the electrical force \( F \) is directly proportional to the product of the charges (\( q_1q_2 \)). When considering the force on an object due to a single charge (or when one charge is fixed), the force is directly proportional to the charge of the object (since if we fix \( q_2 \), \( r \), and \( k \), \( F \propto q_1 \)).

Now let's analyze each option:

• "It is inversely proportional to the square of the charge": From Coulomb's Law, the force is inversely proportional to the square of the distance (\( r^2 \)), not the square of the charge. So this is incorrect.
• "It is directly proportional to the square of the charge": The force is directly proportional to the charge (not the square of the charge) as seen from \( F \propto q \) (when other factors are constant). So this is incorrect.
• "It is inversely proportional to the charge": The force increases as the charge increases (from \( F = k\frac{q_1q_2}{r^2} \)), so it is directly proportional, not inversely proportional. So this is incorrect.
• "It is directly proportional to the charge": As per Coulomb's Law, when other factors (like the charge of the other object, distance, and the constant \( k \)) are constant, the electrical force on an object is directly proportional to its charge. This matches our analysis.

Answer:

D. It is directly proportional to the charge.