Question

What is the magnetic field at the centre of a current-carrying loop?

Hint:

The magnetic field at the center of a current-carrying loop is proportional to the current and inversely proportional to the radius of the loop.

Answer 1

Step 1: Understanding the formula.
The magnetic field at the center of a current-carrying loop can be derived from Ampère’s law. For a circular loop of radius \( R \), carrying a current \( I \), the magnetic field at the center is given by: \[ B = \frac{\mu_0 I}{2R} \] where \( \mu_0 \) is the permeability of free space.
Step 2: Formula derivation.
This formula shows that the magnetic field \( B \) at the center of a loop is directly proportional to the current \( I \) and inversely proportional to the radius \( R \). The permeability of free space \( \mu_0 \) is a constant, \( \mu_0 = 4\pi \times 10^{-7} \, \text{T m/A} \).
Step 3: Conclusion.
Thus, the magnetic field at the center of a current-carrying loop is given by \( B = \frac{\mu_0 I}{2R} \).