Magnetic moment is defined as the product of the magnet's pole strength and the distance between the poles (also known as the magnetic length). When a magnetic strip is bent, its magnetic moment changes based on the new configuration.

Consider a straight magnetic strip with a magnetic moment of $$44 \, \text{Am}^2$$. If this strip is bent into a semicircular shape, we need to find the new effective magnetic moment.

The magnetic moment in a straight strip is given by:

$$ M_{\text{straight}} = m \cdot l $$

where:

• $$m$$ is the pole strength
• $$l$$ is the magnetic length

Given $$M_{\text{straight}} = 44 \, \text{Am}^2$$, let's now consider the strip bent into a semicircular shape.

When the strip is bent into a semicircle, the effective distance between the magnetic poles is the diameter of the semicircle. Let's denote the original length of the strip as $$L$$. In a straight line, this length $$L$$ is also the magnetic length. When bent into a semicircle, the length of the arc of the semicircle is still $$L$$.

The circumference of a full circle is given by:

$$ C = 2\pi R $$

Therefore, the length of the arc of a semicircle is:

$$ L = \pi R $$

Solving for $$R$$, we get:

$$ R = \frac{L}{\pi} $$

The diameter of the semicircle (which is the new effective magnetic length, $$l_{\text{new}}$$) is twice the radius:

$$ l_{\text{new}} = 2R = 2 \cdot \frac{L}{\pi} = \frac{2L}{\pi} $$

Now, the new magnetic moment $$M_{\text{new}}$$ is:

$$ M_{\text{new}} = m \cdot l_{\text{new}} = m \cdot \frac{2L}{\pi} $$

We know from the original magnetic strip:

$$ M_{\text{straight}} = m \cdot L = 44 \, \text{Am}^2 $$

Rewriting $$m$$ in terms of the known magnetic moment of the straight strip:

$$ m = \frac{44}{L} $$

Substituting $$m$$ into the new magnetic moment equation:

$$ M_{\text{new}} = \frac{44}{L} \cdot \frac{2L}{\pi} $$

Canceling out $$L$$ from the numerator and the denominator:

$$ M_{\text{new}} = \frac{44 \cdot 2}{\pi} = \frac{88}{\pi} $$

Given $$\pi = \frac{22}{7}$$, we substitute this value into the equation:

$$ M_{\text{new}} = \frac{88 \cdot 7}{22} = 28 \, \text{Am}^2 $$

Therefore, the magnetic moment of the strip when bent into a semicircular shape is $$28 \, \text{Am}^2$$.