Two positively-charged objects are located 0.1 m apart.
How does the value of their mutual electric force change if the distance between them is doubled?
(A) quadruples (B) doubles (C) same (D) halved (E) one-fourth
How does the value of their mutual electric force change if the distance between them is halved?
(A) quadruples (B) doubles (C) same (D) halved (E) one-fourth
How does the value of their mutual electric force change if the charge on one object is doubled?
(A) quadruples (B) doubles (C) same (D) halved (E) one-fourth
How does the value of their mutual electric force change if the charge on both objects is doubled?
(A) quadruples (B) doubles (C) same (D) halved (E) one-fourth
How does the direction of their mutual electric force change if the sign (positive or negative) of one of the charges changes?
(A) same direction as originally (B) opposite direction
How does their mutual electric force change if the sign of both charges changes?
(A) same direction as originally (B) opposite direction
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Now wait a minute. What do you think?
repulsive force = k Q1 Q2 / R^2
hint, if signs the same, repulsion. Like charges repel.
2^2 = 4 so (1/2)^2 = 1/4
To determine how the value of the mutual electric force changes in each scenario, we can use Coulomb's Law. Coulomb's Law states that the 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.
Let's analyze each scenario:
1. If the distance between the objects is doubled:
According to Coulomb's Law, the force between two charged objects is inversely proportional to the square of the distance between them. Thus, if the distance is doubled, the force will decrease by a factor of 2^2 = 4. Therefore, the mutual electric force will be one-fourth of its original value. The correct answer is (E) one-fourth.
2. If the distance between the objects is halved:
Similarly, if the distance is halved, the force will increase by a factor of (1/2)^2 = 4. Therefore, the mutual electric force will be quadrupled. The correct answer is (A) quadruples.
3. If the charge on one object is doubled:
According to Coulomb's Law, the force between two charged objects is directly proportional to the product of their charges. If the charge on one object is doubled, the force will also double. The correct answer is (B) doubles.
4. If the charge on both objects is doubled:
If both charges are doubled, the force will be directly proportional to the square of the charges. Thus, the force will quadruple. The correct answer is (A) quadruples.
5. If the sign of one of the charges changes:
The sign of the charge determines whether the force is attractive or repulsive. If the sign of one charge changes, the force will change direction and become opposite to the original. The correct answer is (B) opposite direction.
6. If the sign of both charges changes:
If the signs of both charges change, the force will still change direction and become opposite to the original. The correct answer is (B) opposite direction.
Remember that Coulomb's Law provides a mathematical relationship to determine the magnitude and direction of the electric force between two charged objects.