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Four very long current carrying wires in the same plane intersect to form a square 40.0 cm on each side as shown in the diagram. What is the magnitude of current I so that the magnetic field at the centre of the square is zero?

Options

  1. A22     A
  2. B38     A
  3. C2     A
  4. D18     A

Correct answer

C. 2     A

Step-by-step solution

Magnitude of the magnetic field at a particular distance x from infinite long wire is given by B = μ 0 I 2 π x For wire A B , B 1 = 20 μ 0 2 π x k ^ .......(i) Due to B C B 2 = μ 0 I 2 π x ( - k ^ ) ......(ii) Due to D C B 3 = 8 μ 0 2 π x ( - k ^ ) ......(iii) Due to A D B 4 = 10 μ 0 2 π x ( - k ^ ) ......(iv) From Equations, (i), (ii), (iii) and (iv) B 1 + B 2 + B 3 + B 4 = 0 [From question] ⇒ 20 μ 0 2 π x - μ 0 I 2 π x = 8 μ 0 2 π x + 10 μ 0 2 π x ⇒ 20 - I = 8 + 10 ⇒ I = 20 - 18 ⇒ I = + 2 A (Positive sign shows t

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