PHY AL MC MAGNETIC FIELD

Let p and q be the angle RPQ and angle RQP respectively.

Magnetic flux density Bp at R due to current at P,
Bp = (uo)I/[2.pi.(0.3a)] where uo is the permeability of free space
The direction is pointing from R to Q (Right Hnad Grip Rule)
Thus, x-component of magnetic flux density, Bpx = (Bp).cos(q)
i.e. Bpx = (uo)I/[2.pi.(0.3a)].cos(q) = (uo)I/[2.pi.(0.3a)].(0.4a/0.5a)

Magnetic flux density Bq at R due to current at Q,
Bq = (uo)I/[2.pi.(0.4a)]
The direction is pointing from R to P (Right Hnad Grip Rule)
Thus, x-component of magnetic flux density, Bqx = -(Bq).cos(p)
[the -ve sign indicates the Bqx is pointing in the -x direction]
i.e. Bqx = -(uo)I/[2.pi.(0.4a)].cos(p) = -(uo)I/[2.pi.(0.4a)].(0.3a/0.5a)

Therefore, the resultant x-component of magnetic flux density
= Bpx + Bqx
= (uo)I/[2.pi.(0.3a)].(0.4a/0.5a) -(uo)I/[2.pi.(0.4a)].(0.3a/0.5a)
= [(uo)I/(2.pi.a)].[0.4/(0.3 x0.5) - 0.3/(0.4x0.5)]
= [(uo)I/(2.pi.a)].(1.17)