For a current-carrying loop, what is the magnetic field at the center if the rad

For a current-carrying loop, what is the magnetic field at the center if the radius is halved?

For a current-carrying loop, what is the magnetic field at the center if the radius is halved?

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.

Magnetic Field of a Current-Carrying Loop – The magnetic field at the center of a circular loop carrying current is given by the formula B = (μ₀ * I) / (2 * R), where B is the magnetic field, μ₀ is the permeability of free space, I is the current, and R is the radius of the loop.
Inverse Proportionality – Understanding that the magnetic field strength is inversely proportional to the radius of the loop, meaning as the radius decreases, the magnetic field strength increases.