Question

The magnetic field at the center of a circular current carrying loop depends on:

• A. Only the radius of the loop
• B. Only the current flowing
• C. Current and radius of the loop
• D. Resistance of the wire only

Hint:

Keep the center field formula in mind: $B = \frac{\mu_0 I}{2r}$. This tells you right away that the magnetic field changes based on both the amount of current ($I$) and the radius ($r$) of the loop.

Answer 1

The Correct Option is C

Concept: The Biot-Savart Law allows us to calculate the magnetic field induction ($B$) generated at the center of a circular wire loop carrying a steady current. The derived formula for a loop with $N$ turns is: \[ B = \frac{\mu_0 N I}{2 r} \] Where:
• $\mu_0$ is the permeability of free space constant ($4\pi \times 10^{-7}\text{ T}\cdot\text{m/A}$).
• $N$ is the number of turns in the circular wire loop.
• $I$ is the electric current flowing through the loop.
• $r$ is the radius of the circular loop.

Step 1: Isolate the operational variables.
From the formula, we can see that for a given loop configuration, the magnetic field strength depends directly on two main physical properties:
• It is directly proportional to the current ($I$) flowing through the wire ($B \propto I$).
• It is inversely proportional to the radius ($r$) of the circular loop ($B \propto \frac{1}{r}$). Therefore, the magnetic field at the center depends on both the Current and the radius of the loop.