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A symmetric star shaped conducting wire ...

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

A

`(mu_0I)/(4pia)6[sqrt3-1]`

B

`(mu_0I)/(4pia)6[sqrt3+1]`

C

`(mu_0I)/(4pia)3[2-sqrt3]`

D

`(mu_0I)/(4pia)3[sqrt3-1]`

Text Solution

Verified by Experts

The correct Answer is:
A

Total Magnetic Field at centre = 12 times magnetic field due to one wire
`B=(12mu_0I)/(4pia)[ sin 60^@- sin 30^@] =(mu_0I)/(4pia)xx12[sqrt3/2-1/2]`
`implies B =(mu_0I)/(4pia)xx6(sqrt3-1)`
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