To produce a magnetic field of `pi` tesla at the centre of circular loop of diameter 1 m, the current flowing through loop is :

Options

A. `5xx10^(6)A`
B. `10^(7)A`
C. `2.5xx10^(6)A`
D. `2xx10^(6)A`

Answer

To find the current flowing through a circular loop that produces a magnetic field of \( \pi \) Tesla at its center, we can use the formula for the magnetic field at the center of a circular loop:

\[ B = \frac{\mu_0 I}{2R} \]

Where:
- \( B \) is the magnetic field (in Tesla),
- \( \mu_0 \) is the permeability of free space (\( 4\pi \times 10^{-7} \, \text{T m/A} \)),
- \( I \) is the current (in Amperes),
- \( R \) is the radius of the loop (in meters).

### Step 1: Identify the given values
- Magnetic field \( B = \pi \, \text{T} \)
- Diameter of the loop = 1 m, hence the radius \( R = \frac{1}{2} \, \text{m} = 0.5 \, \text{m} \)

### Step 2: Substitute the values into the formula
We can rearrange the formula to solve for current \( I \):

\[ I = \frac{2BR}{\mu_0} \]

Substituting the known values:

\[ I = \frac{2 \cdot \pi \cdot 0.5}{4\pi \times 10^{-7}} \]

### Step 3: Simplify the equation
The \( \pi \) in the numerator and denominator cancels out:

\[ I = \frac{2 \cdot 0.5}{4 \times 10^{-7}} = \frac{1}{4 \times 10^{-7}} \]

### Step 4: Calculate the current
Now, we can calculate \( I \):

\[ I = \frac{1}{4 \times 10^{-7}} = 2.5 \times 10^{6} \, \text{A} \]

### Final Answer
Thus, the current flowing through the loop is:

\[ I = 2.5 \times 10^{6} \, \text{A} \]

### Options
The correct option based on the calculated current is option 3: \( 2.5 \times 10^{6} \, \text{A} \).

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