Current `I` flows through the circuit, as shown. Find the magnetic moment of the figure, if `AB=BC=CD=DE=EF=FG=GH=HA`:

Options

A. `(7)/(2)Ipia^(2)`
B. `(5)/(2)Ipia^(2)`
C. `4Ipia^(2)`
D. `(5)/(3)Ipia^(2)`

Answer

B

Explanation

Angle `theta` for one segment,
`theta=(2pi)/(8)=(pi)/(4)M_(0)=IA=I[r^(2)(theta)/(2)-r_(1)^(2)(theta)/(2)]`
`= I[(2a^(2))(theta)/(2)-a^(2)(theta)/(2)]=I.(3a^(2)theta)/(2)`
For `4` segments, `M=4I.3a^(2)(theta)/(2)=6Ia^(2)theta`
Magnetic moment due to circle `=I pia^(2)`
Total magnetic moment
`=6Ia2theta+Ipia^(2)=6Ia^(2)xx(pi)/(4)+I.pia^(2)=(5)/(2)Ipia^(2)`