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)/(4 pi a) 6[ sqrt3 - 1]`
B. `(mu_(0)I)/(4 pi a) 6[sqrt3 + 1]`
C. `(mu_(0)I)/(4 pi a) 3[2 - sqrt3]`
D. `(mu_(0)I)/(4 pi a) 3[ sqrt3 - 1]`

Answer

a

Explanation

Total Magnetic Field at centre = 12 times magnetic field due to one wire
`B = (12 mu_(0)I)/(4 pi a) [ sin 60^(@) - sin 30^(@)] = (mu_(0)I)/(4 pi a) xx 12 [sqrt3/2 - 1/2]`
`rArr B = (mu_(0)I)/(4 pi a) xx 6 (sqrt3 - 1)`
Hence option (a) is correct.