The magnetic field existing in a region is given by `vecB =B_0(1+(x)/(l))vec k.` A square loop of edge l and carrying a current I, is placed with its edges parallel to the x-y axes. Find the magnitude of the net magnetic force experienced by the loop.

Explanation

To solve the problem, we need to find the net magnetic force experienced by a square loop carrying a current \( I \) in a magnetic field defined by \( \vec{B} = B_0 \left(1 + \frac{x}{l}\right) \hat{k} \). The loop has edges of length \( l \) and is oriented parallel to the x-y axes.

### Step-by-Step Solution:

1. **Understanding the Magnetic Field**:
The magnetic field varies with the x-coordinate and is given by:
\[
\vec{B} = B_0 \left(1 + \frac{x}{l}\right) \hat{k}
...