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)4πaμ0I6[3−1]✓ Correct
(B)4πaμ0I6[3+1]
(C)4πaμ0I3[3−1]
(D)4πaμ0I3[2−3]
Answer: (A)
Solution
The star has 12 straight segments. Each segment contributes to the magnetic field at the center. Using Biot-Savart law for a finite wire segment at distance a from the center, with angles 60° and 30° from the perpendicular: B=12⋅4πaμ0I(sin60°−sin30°)=4πaμ0I⋅12⋅(23−21)=4πaμ0I⋅6(3−1).
JEE Advanced · 2017 · 21 May 2017 · Paper 2 · Single correct option