Coulomb\'s Law Force Relationships

According to Coulomb's law, the electric force between two charges is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them. If one charge is doubled and the other is quadrupled, the product of the charges increases by a factor of 8 (2 x 4). Additionally, reducing the distance to half increases the force by a factor of 4 (1/(1/2)^2). Multiplying these factors (8 x 4) results in an increase of the electric force by a factor of 32.

According to Coulomb's Law, the electrostatic force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. When you triple the charge of one object while keeping the other charge and the distance constant, the force increases proportionally to the increase in charge. Therefore, tripling one charge results in the force also increasing by a factor of 3, as the distance remains unchanged.

According to Coulomb's law, the electric force between two charges is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them. If one charge is halved, the force decreases by a factor of 2. Doubling the distance increases the denominator in the equation, reducing the force by a factor of 4 (since \(2^2 = 4\)). Combining these effects results in a total decrease of \(2 \times 4 = 8\), leading to an overall reduction of the electric force by a factor of 8.

When you reduce the charge of one object to one-fifth of its original value while keeping the other object's charge and the distance between them constant, the electrostatic force between the two objects is directly proportional to the product of their charges. According to Coulomb's Law, if one charge decreases by a factor of 5, the overall force also decreases by the same factor, resulting in a reduced force that is one-fifth of the original force. Therefore, the statement is true.

According to Coulomb's law, the electric force between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. If both charges are tripled, the force increases by a factor of 3 × 3 = 9. Reducing the distance to one-third increases the force by a factor of (1/(1/3)²) = 9. Therefore, the total increase in force is 9 × 9 = 81, resulting in an overall increase by a factor of 81.

According to Coulomb's law, the electrostatic force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. If you reduce the charge of one object to one-eighth, the force will decrease by the same factor because the distance remains unchanged. Therefore, the force between the objects decreases by a factor of 8, reflecting the change in charge.

According to Coulomb's Law, the electric force \( F \) between two charges is given by \( F = k \frac{q_1 q_2}{r^2} \), where \( k \) is a constant, \( q_1 \) and \( q_2 \) are the magnitudes of the charges, and \( r \) is the distance between them. If you quadruple one charge (increase by a factor of 4) and triple the distance (increase by a factor of 3), the new force becomes \( F' = k \frac{4q_1 q_2}{(3r)^2} = k \frac{4q_1 q_2}{9r^2} \). Thus, the force increases by a factor of \( \frac{4}{9} \).

According to Coulomb's law, the electrostatic force between two charges is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them. If you double one charge, it becomes 2q, and if you reduce the distance to 1/4, the new distance squared becomes (1/4)² = 1/16. Thus, the force increases by a factor of (2 * 1)/(1/16) = 32. Therefore, the overall force increases by a factor of 32.