Question

If the current $ I $ flows through the coil of radius $ r $, then the field at the center of the circular coil is

• A. Inversely proportional to \( I^2 \)
• B. Directly proportional to \( I \)
• C. Directly proportional to \( r \)
• D. Inversely proportional to \( r^2 \)

Hint:

The magnetic field at the center of a circular coil is directly proportional to the current and inversely proportional to the radius of the coil.

Answer 1

The Correct Option is B

Step 1: Magnetic Field Due to a Circular Coil
The magnetic field at the center of a circular coil carrying a current is given by the formula: \[ B = \frac{\mu_0 I}{2r} \] Where:
\( B \) is the magnetic field,
\( \mu_0 \) is the permeability of free space,
\( I \) is the current,
\( r \) is the radius of the coil.

Step 2: Conclusion
From the formula, we can see that the magnetic field at the center of the coil is directly proportional to the current \( I \) and inversely proportional to the radius \( r \).
Therefore, the correct answer is that the field is directly proportional to \( I \).