An element `dvecl=dxhati` (where `dx=1cm`) is placed at the origin and carries a large current `i=10A`. What is the magnetic field on the Y-axis at a distance of `0.5m`?

Explanation

To find the magnetic field at a point on the Y-axis due to a current-carrying element, we can use the Biot-Savart Law. Here’s a step-by-step solution:

### Step 1: Understand the setup
We have a current element \( \vec{dl} = dx \hat{i} \) at the origin carrying a current \( i = 10 \, A \). We want to find the magnetic field at a point on the Y-axis, specifically at a distance \( y = 0.5 \, m \).

### Step 2: Convert units
Since \( dx = 1 \, cm = 0.01 \, m \), we will use this value in our calculations.

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