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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 4 a .

Options

  1. Aμ 0 I 4 π a 3 3 - 1
  2. Bμ 0 I 4 π a 6 3 - 1
  3. Cμ 0 I 4 π a 6 3 + 1
  4. Dμ 0 I 4 π a 3 2 - 3

Correct answer

B. μ 0 I 4 π a 6 3 - 1

Step-by-step solution

The given points (1, 2, 3, 4, 5, 6) makes 360 o angle at ‘O’. Hence angle made by vertices 1 and 2 with ‘O’ is 60 o . Direction of magnetic field at ‘O’ due to each segment is same. Since it is symmetric star shape, magnitude will also be same. Magnetic field due to section BC. B 1 = k i a sin ⁡ 60° - sin ⁡ 30° = k i 2 a 3 - 1 B n e t = 12 × B 1 = 6 k i a 3 - 1 a n d k = μ 0 4 π

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