Answer:
The value is [tex]B = 3.33 *10^{-6} \ T[/tex]
Explanation:
From the question we are told that
The distance of separation is [tex]d = 0.6 \ m[/tex]
The current on the one wire is [tex]I_1 = 9 \ A[/tex]
The current on the second wire is [tex]I_2 = 4 \ A[/tex]
Generally the magnitude of the field exerted between the current carrying wire is
[tex]B = B_1 - B_2[/tex]
Here [tex]B_1[/tex] is the magnetic field due to the first wire which is mathematically represented as
[tex]B_1 = \frac{\mu_o * I_1 }{2 \pi * d_1}[/tex]
Here [tex]d_1[/tex] is the distance to the half way point of the separation and the value is
[tex]d_1 = 0.3 \ m[/tex]
[tex]B_2[/tex] is the magnetic field due to the first wire which is mathematically represented as
[tex]B_2 = \frac{\mu_o * I_2 }{2 \pi * d_2}[/tex]
Here [tex]d_2[/tex] is the distance to the half way point of the separation and the value is
[tex]d_2 = 0.3 \ m[/tex]
This means that [tex]d_1 = d_2 = a = 0.3[/tex]
So
[tex]B = \frac{\mu_o * I_1 }{2 \pi * d_1} - \frac{\mu_o * I_2 }{2 \pi * d_2}[/tex]
=> [tex]B = \frac{\mu_o * (I_1 - I_2)}{2 \pi *0.3 }[/tex]
=> [tex]B = \frac{ 4\pi * 10^{-7} * (9- 4)}{2 * 3.142 *0.3 }[/tex]
=> [tex]B = 3.33 *10^{-6} \ T[/tex]
