Question

Magnetic field at the centre of a circular coil of radius \( r \), through which a current \( I \) flows is:

• A. directly proportional to \( r \)
• B. inversely proportional to \( I \)
• C. directly proportional to \( I \)
• D. directly proportional to \( I^2 \)

Hint:

The magnetic field at the centre of a circular coil is directly proportional to the current and inversely proportional to the radius of the coil. The formula is \( B = \frac{\mu_0 I}{2 r} \).

Answer 1

The Correct Option is C

Step 1: Formula for Magnetic Field at the Centre of a Circular Coil
The magnetic field at the centre of a circular coil carrying a current \( I \) is given by the formula: \[ B = \frac{\mu_0 I}{2 r} \] where:
\( \mu_0 \) is the permeability of free space,
\( I \) is the current flowing through the coil,
\( r \) is the radius of the coil.
Step 2: Analyzing the Dependence of Magnetic Field
From the formula, we can see that the magnetic field at the centre is directly proportional to the current \( I \) and inversely proportional to the radius \( r \).
Therefore, the magnetic field is directly proportional to \( I \) and not to \( r \), nor is it proportional to \( I^2 \). Final Answer: The magnetic field at the centre of the circular coil is directly proportional to \( I \).