question_answer

The effective length of a magnet is 31.4 cm and its pole strength is 0.5 A-m. The magnetic moment, if it is bent in the form of a semicircle will be:

A)  \[0.1\,\,A-{{m}^{2}}\]

B)  \[0.01\,\,A-{{m}^{2}}\]

C)  \[0.2\,\,A-{{m}^{2}}\]

D)  \[1.2\,\,A-{{m}^{2}}\]

Correct Answer: A

Solution :

 Key Idea: Circumference of a circle of radius r is \[2\,\pi r\]. Magnetic moment (M) is a measure of the strength of a magnetic source. It is denned as pole strength (m) multiplied by distance (d) \[M=md\] Circumference of semicircle is \[\pi \frac{d}{2}\]. Given, \[d=31.4\,cm=31.4\times {{10}^{-2}}m\] \[l=\frac{\pi d}{2}\] \[0.314=\frac{3.14}{2}\times d\] \[\Rightarrow \] \[d=0.2\,m\]. So, magnetic moment \[=0.5\times 0.2=0.1\,\,A-{{m}^{2}}\],