If the distance between two charges is halved, how does the force between them change?
Practice Questions
1 question
Q1
If the distance between two charges is halved, how does the force between them change?
It doubles
It quadruples
It remains the same
It halves
According to Coulomb's law, the force F between two charges is inversely proportional to the square of the distance. If the distance is halved, the force becomes four times greater.
Questions & Step-by-step Solutions
1 item
Q
Q: If the distance between two charges is halved, how does the force between them change?
Solution: According to Coulomb's law, the force F between two charges is inversely proportional to the square of the distance. If the distance is halved, the force becomes four times greater.
Steps: 8
Step 1: Understand Coulomb's law, which states that the force (F) between two charges is related to the distance (d) between them.
Step 2: Remember that the formula for the force is F = k * (q1 * q2) / d^2, where k is a constant and q1 and q2 are the charges.
Step 3: Note that 'd' is in the denominator and is squared (d^2). This means that if 'd' changes, the force will change significantly.
Step 4: If the distance (d) is halved, it becomes d/2.
Step 5: Substitute d/2 into the formula: F = k * (q1 * q2) / (d/2)^2.
Step 6: Simplify the equation: (d/2)^2 = d^2 / 4, so F = k * (q1 * q2) / (d^2 / 4).
Step 7: This can be rewritten as F = k * (q1 * q2) * (4 / d^2).
Step 8: Notice that the force is now 4 times greater than the original force when the distance was d.
