For a current-carrying loop, what is the magnetic field at the center if the radius is halved?
Practice Questions
1 question
Q1
For a current-carrying loop, what is the magnetic field at the center if the radius is halved?
It remains the same
It doubles
It quadruples
It halves
The magnetic field at the center of a loop is inversely proportional to the radius. If the radius is halved, the magnetic field quadruples.
Questions & Step-by-step Solutions
1 item
Q
Q: For a current-carrying loop, what is the magnetic field at the center if the radius is halved?
Solution: The magnetic field at the center of a loop is inversely proportional to the radius. If the radius is halved, the magnetic field quadruples.
Steps: 6
Step 1: Understand that a current-carrying loop creates a magnetic field around it.
Step 2: Know that the strength of the magnetic field at the center of the loop depends on the radius of the loop.
Step 3: Remember that the magnetic field (B) is inversely proportional to the radius (r) of the loop. This means that if the radius decreases, the magnetic field increases.
Step 4: If the radius is halved (r becomes r/2), we can express this relationship mathematically: B ∝ 1/r.
Step 5: When the radius is halved, the new radius is r/2, so the magnetic field becomes B' = k/(r/2) = 2k/r, where k is a constant.
Step 6: Since B = k/r, we can see that B' = 4B, meaning the magnetic field quadruples when the radius is halved.
