Question

Four long parallel wires pass through the corners of a square with side 0.62 m. All four wires carry the same magnitude of current I = 24.1 A in the directions indicated. Find the magnetic field at point P, the midpoint of the top side of the square.

Four long parallel wires pass through the corners of a square with side 0.62 m. All four wires carry the same magnitude of current I = 24.1 A in the directions indicated. Find the magnetic field at point P, the midpoint of the top side of the square.

Answer 1

ED = 0.31 m , CD = 0.62 m

0.613 12 Magnetic field by wire at B:: B, =(10-7) 2 (24.12 = 69.6 x、-"r

In triangle EDC

ED = 0.31 m   , CD = 0.62

so tan$\theta$ = CD/ ED = 0.62 /0.31

$\theta$ = 63.4

B₁ and B₂ are making angle $\theta$ with the upper side of the square at P as shown

vertical Component of B₁ = B₁ sin$\theta$   in Up

vertical Component of B₂ = B₂ sin$\theta$   in down

So The vertical components of magnetic field cancel out being in opposite direction and horizontal component adds to give total magnetic field as

B_total = B₁ Cos$\theta$ + B₂ Cos$\theta$

B₁ = B₂

so Btotal = B₁ Cos$\theta$ + B₁ Cos$\theta$ = 2 B₁ Cos$\theta$ = 2 x (69.6 x 10^-7 T) Cos 63.4 = 62.33 x 10^-7 T