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 I pi a^(2)`
B. `5/2 I pi a^(2)`
C. `4 I pi a^(2)`
D. `5/3 I pi a^(2)`

Answer

B

Explanation

Angle `theta` for one segment, `theta=(2pi)/(8)=(pi)/(4)`
`(M_0)=IA=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 segment, `M=4I*3a^(2)=6Ia^(2)theta`
Magnetic moment due to circle `=I pi a^(2)`
Total magnetic moment `=6Ia^(2) theta +Ipi a^(2)1`
`=6Ia^(2) xx (pi)/(4) + I*pi a^(2)=5/2 I pi a^(2)`.