(a) Write, using Biot-Savart law, the expression for the magnetic field `vecB` due to an element `vecdl` carrying current I at a distance `vecr` from it in a vector form.
Hence ,derive the expression for the magnetic field due to a current carring loop of radius R at a point P distant x from its centre along the axis of the loop.

Explanation

To solve the problem, we will follow a structured approach to derive the expression for the magnetic field \( \vec{B} \) due to a current-carrying loop using Biot-Savart law.

### Step 1: Write Biot-Savart Law in Vector Form
The Biot-Savart law states that the magnetic field \( d\vec{B} \) at a point in space due to a small current element \( d\vec{l} \) carrying current \( I \) is given by:

\[ d\vec{B} = \frac{\mu_0}{4\pi} \frac{I \, d\vec{l} \times \hat{r}}{r^2} \]
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