Two identical charges are placed 1 m apart. If the distance is reduced to 0.5 m, how does the force between them change? (2022)
Practice Questions
1 question
Q1
Two identical charges are placed 1 m apart. If the distance is reduced to 0.5 m, how does the force between them change? (2022)
It doubles
It remains the same
It quadruples
It halves
According to Coulomb's law, F ∝ 1/r². Reducing the distance to half increases the force by a factor of 4.
Questions & Step-by-step Solutions
1 item
Q
Q: Two identical charges are placed 1 m apart. If the distance is reduced to 0.5 m, how does the force between them change? (2022)
Solution: According to Coulomb's law, F ∝ 1/r². Reducing the distance to half increases the force by a factor of 4.
Steps: 6
Step 1: Understand that we have two identical charges placed 1 meter apart.
Step 2: Recall Coulomb's law, which states that the force (F) between two charges is inversely proportional to the square of the distance (r) between them. This means F ∝ 1/r².
Step 3: Identify the initial distance (r1) as 1 meter. Calculate the initial force (F1) using the formula: F1 ∝ 1/(1 m)² = 1.
Step 4: Now, reduce the distance to 0.5 meters (r2 = 0.5 m). Calculate the new force (F2) using the formula: F2 ∝ 1/(0.5 m)².
Step 5: Calculate (0.5 m)², which is 0.25. Therefore, F2 ∝ 1/0.25 = 4.
Step 6: Compare the forces: Since F2 is 4 times greater than F1, reducing the distance to half increases the force by a factor of 4.
