Question

A magnetic field intensity at the centre of a circular wire of radius 0.1 m carrying a current 0.2 A is:

• A. \( 2\pi \times 10^{-5} \, T \)
• B. \( \pi \times 10^{-7} \, T \)
• C. \( 10^{-7} \, T \)
• D. \( 4\pi \times 10^{-7} \, T \)

Hint:

Always use the formula for the magnetic field at the center of a circular loop and remember to substitute values carefully.

Answer 1

The Correct Option is D

The magnetic field intensity at the centre of a circular loop is given by the formula: \[ B = \frac{\mu_0 I}{2r} \] where:

• \( B \) is the magnetic field intensity,
• \( \mu_0 = 4\pi \times 10^{-7} \, T \cdot m/A \) is the permeability of free space,
• \( I = 0.2 \, A \) is the current, and
• \( r = 0.1 \, m \) is the radius of the circular loop.

Substituting the given values into the formula: \[ B = \frac{4\pi \times 10^{-7} \times 0.2}{2 \times 0.1} = 4\pi \times 10^{-7} \, T \] Thus, the magnetic field intensity is \( 4\pi \times 10^{-7} \, T \).

Answer 2

Step 1: Use the formula for magnetic field at the center of a circular loop.
The magnetic field at the center of a circular current-carrying wire is given by:
\[ B = \frac{\mu_0 I}{2R} \] where:
- \( B \) is the magnetic field (in Tesla),
- \( \mu_0 = 4\pi \times 10^{-7} \, \text{Tm/A} \) (permeability of free space),
- \( I = 0.2 \, \text{A} \) (current),
- \( R = 0.1 \, \text{m} \) (radius).

Step 2: Substitute the values into the formula.
\[ B = \frac{4\pi \times 10^{-7} \times 0.2}{2 \times 0.1} = \frac{4\pi \times 0.2 \times 10^{-7}}{0.2} = 4\pi \times 10^{-7} \, \text{T} \]

Step 3: Conclusion.
The magnetic field intensity at the center of the circular wire is \( \boxed{4\pi \times 10^{-7} \, \text{T}} \).