A symmetric star shaped conducting wire loop is carrying a steady state current I as shown in the figure. The distance between the diametrically opposite vertices of the star is 4a. The magnitude of the magnetic field at the center of the loop is

Options

A. `(mu_(0)I)/(4pia)6 [ sqrt(3)-1]`
B. `(mu_(0)I)/(4pia)3 [sqrt(3)-1]`
C. `(mu_(0)I)/(4pia)6[sqrt(3)+1]`
D. `(mu_(0)I)/(4pia)3[2-sqrt(3)]`

Answer

D

Explanation

Magnetic field due to one section of star can be calculated as follows
`B_(0)=(mu_(0)i)/(4pia)[sin 60^(@)-sin 30^(@)]`
`B_(0)=(mu_(0)i)/(4pia) ((sqrt(3)-1)/2)`
Total field `B=12B_(0)`
`=(mu_(0)i)/(2pia)3(sqrt(3)-1)`