Question

Four long parallel wires are arranged at the four comers of a square ABCD of side 20 cm. Each wire carries a current of 5 A. Currents in the conductors 1 and 2, at comers A and B, are out of the page while those in the conductors 3 and 4, at comers C and D, are into the page. What is the magnitude of the magnetic induction at the centre of the square?

Answer 1

Data : 2l = 20 cm = 0.2 m, I = 5 A

If each side of the square array is 2l, then from geometry, the centre of the square O is a distance \(\sqrt{2I}\) from each corner. Since each wire carries the same current, B₁ = B₂ = B₃ = B₄ . Using the right hand [grip] rule, the directions of the magnetic inductions due to conductors 1 and 3 are along OB, while those due to conductors 2 and 4 are along OC, as shown.

The magnitude of the magnetic induction along OB is

This is also the magnitude of the magnetic induction along OC, B₂ + B₄.

Their components parallel to AD (or BC) are oppositely directed and cancel out. Therefore, the total induction at the centre of the square has a magnitude equal to the sum of the components parallel to AB (or DC).

\(\vec B\) is directed towards the right.

The magnitude of the magnetic induction at the centre of the square is 2 × 10^-5 T.