A tightly wound 100 turns coil of radius 10 cm carries a current of 7 A. The magnitude of the magnetic field at the centre of the coil is (Take permeability of free space as 4π × 10^–7 SI units) :

**Step 1 – Identify the formula**
For a circular coil of radius R carrying N turns of current I, the magnetic field at the centre is

$B\; =\; \backslash frac\{\backslash mu\_0\; N\; I\}\{2R\}$

where μ₀ = 4π × 10⁻⁷ T·m/A (permeability of free space).

**Step 2 – Convert all quantities to SI units**
Radius R = 10 cm = 0.10 m
Number of turns N = 100
Current I = 7 A

**Step 3 – Plug the numbers into the formula**

$B\; =\; \backslash frac\{(4\backslash pi\; \backslash times\; 10^\{-7\}\backslash ,\backslash text\{T·m/A\})\; \backslash times\; 100\; \backslash times\; 7\backslash ,\backslash text\{A\}\}\{2\; \backslash times\; 0.10\backslash ,\backslash text\{m\}\}$

**Step 4 – Simplify the expression**

$\backslash frac\{100\; \backslash times\; 7\}\{2\; \backslash times\; 0.10\}\; =\; \backslash frac\{700\}\{0.20\}\; =\; 3500$

Hence

$B\; =\; (4\backslash pi\; \backslash times\; 10^\{-7\})\; \backslash times\; 3500$

**Step 5 – Perform the multiplication**

$4\; \backslash times\; 3500\; =\; 14000$

So

$B\; =\; 14000\backslash pi\; \backslash times\; 10^\{-7\}\backslash ,\backslash text\{T\}$

Convert the power of ten:

$14000\; \backslash times\; 10^\{-7\}\; =\; 1.4\; \backslash times\; 10^\{-3\}$

Therefore

$B\; =\; 1.4\; \backslash times\; 10^\{-3\}\backslash ,\backslash pi\backslash \; \backslash text\{T\}$

**Step 6 – Approximate π (≈ 3.1416)**

$B\; \backslash approx\; 1.4\; \backslash times\; 10^\{-3\}\; \backslash times\; 3.1416\backslash \; \backslash text\{T\}\; \backslash approx\; 4.398\; \backslash times\; 10^\{-3\}\backslash \; \backslash text\{T\}$

**Step 7 – Express in millitesla**

$4.398\; \backslash times\; 10^\{-3\}\backslash \; \backslash text\{T\}\; =\; 4.398\backslash \; \backslash text\{mT\}\; \backslash approx\; 4.4\backslash \; \backslash text\{mT\}$

**Conclusion**
The magnetic field at the centre of the coil is **4.4 mT**, which matches the given correct option.