Question

The current that has to pass through a single circular loop of radius 10 cm to produce a magnetic field of \(\mu_0\) tesla at its centre is

• A. 1 A
• B. 0.2 A
• C. 0.4A
• D. 0. 5A
• E. 0.3A

Hint:

Always convert the radius to meters before performing calculations.
10 cm = 0.1 m.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The magnetic field (\( B \)) at the center of a circular loop of radius \( R \) carrying current \( I \) is given by the Biot-Savart Law.

Step 2: Key Formula or Approach:
\[ B = \frac{\mu_0 I}{2R} \]

Step 3: Detailed Explanation:
Given:
Magnetic field \( B = \mu_0 \text{ T} \)
Radius \( R = 10 \text{ cm} = 0.1 \text{ m} \)
Substituting into the formula:
\[ \mu_0 = \frac{\mu_0 I}{2(0.1)} \]
The term \( \mu_0 \) cancels out from both sides:
\[ 1 = \frac{I}{0.2} \]
\[ I = 0.2 \text{ A} \]

Step 4: Final Answer:
The required current is 0.2 A.