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Q.

Four very long, current carrying wires in the same plane intersect to form a square 40.0 cm on each side, as shown in figure. Find the magnitude and direction of the current I so that the magnetic field at the center of the square is zero.

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a

4.0 A toward the bottom of the page.

b

2.0 A toward the bottom of the page.

c

2.5 A toward the bottom of the page.

d

3.6 A toward the top of the page.

answer is B.

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Detailed Solution

B∝I, because distance of centre for all wires is zero.  B1=kI1=10k⊗,B2=kI2=8k⊗ B3=kI3=20k⊙,B4=kI4  Now B1+B2+B3+B4=0 ⇒  (10k+8k-20k)⊗+kI4=0 ⇒  kI4=2k⊗ ⇒  I4=2 A towards the bottom.
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