A wire of length l has a magnetic moment M. Another wire of same length and magnetic moment is taken and is bent into a semicircular arc. Find the ratio of magnetic moment of wire to that of the semicircular arc.

Explanation

To solve the problem of finding the ratio of the magnetic moment of a straight wire to that of a semicircular arc formed from the same wire, we will follow these steps:

### Step 1: Understand the Magnetic Moment of the Straight Wire
The magnetic moment \( M \) of a straight wire of length \( l \) can be defined as:
\[ M = Q_m \cdot l \]
where \( Q_m \) is the pole strength. Since the magnetic moment is given as \( M \), we can express the pole strength as:
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