A straight magnetic strip has a magnetic moment of $44 \mathrm{~Am}^2$. If the strip is bent in a semicircular shape, its magnetic moment will be ________ $\mathrm{Am}^2$.

(given $\pi=\frac{22}{7}$)

<p>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.</p> <p>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.</p> <p>The magnetic moment in a straight strip is given by:</p> <p>$M_{\text{straight}} = m \cdot l$</p> <p>where:</p> <ul> <li>$m$ is the pole strength</li> <li>$l$ is the magnetic length</li> </ul> <p>Given $M_{\text{straight}} = 44 \, \text{Am}^2$, let's now consider the strip bent into a semicircular shape.</p> <p>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 $L$.</p> <p>The circumference of a full circle is given by:</p> <p>$C = 2\pi R$</p> <p>Therefore, the length of the arc of a semicircle is:</p> <p>$L = \pi R$</p> <p>Solving for $R$, we get:</p> <p>$R = \frac{L}{\pi}$</p> <p>The diameter of the semicircle (which is the new effective magnetic length, $l_{\text{new}}$) is twice the radius:</p> <p>$l_{\text{new}} = 2R = 2 \cdot \frac{L}{\pi} = \frac{2L}{\pi}$</p> <p>Now, the new magnetic moment $M_{\text{new}}$ is:</p> <p>$M_{\text{new}} = m \cdot l_{\text{new}} = m \cdot \frac{2L}{\pi}$</p> <p>We know from the original magnetic strip:</p> <p>$M_{\text{straight}} = m \cdot L = 44 \, \text{Am}^2$</p> <p>Rewriting $m$ in terms of the known magnetic moment of the straight strip:</p> <p>$m = \frac{44}{L}$</p> <p>Substituting $m$ into the new magnetic moment equation:</p> <p>$M_{\text{new}} = \frac{44}{L} \cdot \frac{2L}{\pi}$</p> <p>Canceling out $L$ from the numerator and the denominator:</p> <p>$M_{\text{new}} = \frac{44 \cdot 2}{\pi} = \frac{88}{\pi}$</p> <p>Given $\pi = \frac{22}{7}$, we substitute this value into the equation:</p> <p>$M_{\text{new}} = \frac{88 \cdot 7}{22} = 28 \, \text{Am}^2$</p> <p>Therefore, the magnetic moment of the strip when bent into a semicircular shape is $28 \, \text{Am}^2$.</p>