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A straight magnetic strip has a magnetic moment of 44 \( \text{Am}^2\) . If the strip is bent in a semicircular shape, its magnetic moment will be ………. \(\text{Am}^2\). (Given \( \pi=\frac{22}{7}\))  

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Best answer

Correct answer is :  28 

A straight magnetic strip has a magnetic 

We know that, pole strength \(\mathrm{m}=\frac{\mathrm{M}}{\mathrm{l}}\) 

\( \begin{aligned} =\mathrm{M}=\mathrm{ml} \end{aligned} \)

\( \begin{aligned} \Rightarrow \mathrm{M}=\mathrm{m} \times 2 \mathrm{r} \end{aligned} \) 

If r is the radius of semicircle formed by bending the strip of length 1 , then 

\( \begin{aligned} \pi \mathrm{r}=1 \end{aligned} \) 

\( \begin{aligned} \mathrm{r}=\frac{1}{\pi} \end{aligned} \)  

Distance b/w the poles ; \(2 \mathrm{r}=\frac{21}{\pi}\) 

Hence, new magnetic moment \(\left(\mathrm{M}^{\prime}\right)\) 

\( \begin{aligned} M^{\prime}=m \times 1 \end{aligned} \) 

\( \begin{aligned} =\frac{M}{l} \cdot \frac{2 l}{\pi}=\frac{2 M}{\pi}=\frac{2 \times 44}{(22 / 7)} \end{aligned} \) 

\( \begin{aligned} =28 \mathrm{Am}^2 \end{aligned} \)  

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