Derive the expression for the torque `tau` acting on a rectangular current loop of area A placed in a uniform magnetic field B. Show that ` vec tau=vecmxx vec B` where `vecm` is the moment of the current loop given by `vecm =vecIA`.

Explanation

To derive the expression for the torque \( \tau \) acting on a rectangular current loop of area \( A \) placed in a uniform magnetic field \( B \), we will follow these steps:

### Step 1: Define the Current Loop and Magnetic Field
Consider a rectangular current loop with area \( A \) and a current \( I \) flowing through it. The loop is placed in a uniform magnetic field \( \vec{B} \). Let the loop be oriented such that its sides are parallel to the axes.

### Step 2: Calculate the Forces on the Loop
The forces acting on the segments of the loop can be analyzed. The force \( \vec{F} \) on a segment of wire carrying current \( I \) in a magnetic field \( \vec{B} \) is given by:
\[
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