Complete Question
The diagram for this question is shown on the first uploaded image
Answer:
The value is [tex]B_A = 8*10^{-5} \ T[/tex]
Explanation:
From the diagram we see that
The distance of the magnetic field generated by first wire to point a is
[tex]l_1 = 2 \ cm = 0.02 \ m[/tex]
The distance of the magnetic field generated by second wire to point a is
[tex]l_2 = 4 + 2 =6 \ cm = 0.06 \ m[/tex]
Let the current passing through both wire be [tex]I_1 = I_2 = I = 12 \ A[/tex]
Generally the the magnetic field strength at point a is mathematically represented as
[tex]B_A = \frac{\mu_o * I_1 }{ 2 * \pi * l_1 } - \frac{\mu_o * I_1 }{ 2 * \pi * l_2 }[/tex]
=> [tex]B_A = \frac{\mu_o }{ 2 * \pi } * [\frac{I_1 }{ l_1 } - \frac{I_2}{l_2} ][/tex]
Generally [tex]\mu_o[/tex] is the permeability of free space with value [tex]\mu_o = 4\pi * 10^{-7} N/A^2[/tex]
[tex]B_A = \frac{ 4\pi * 10^{-7} }{ 2 * 3.142 } * [\frac{12}{ 0.02} - \frac{12}{0.06} ][/tex]
=> [tex]B_A = 8*10^{-5} \ T[/tex]
The magnetic field strength at point a will be [tex]\rm B_a = 8 \times 10^{-5} \ T[/tex].
The number of magnetic flux lines on a unit area passing perpendicular to the given line direction is known as magnetic field strength .it is denoted by B.
The distance between point a and the magnetic field created by the first wire is;
[tex]\rm L_1 = 2 \ cm= 0.02 \ cm[/tex]
The distance between point a and the magnetic field created by the second wire is;
[tex]\rm L_2 = 4+2 = 6 cm = 0.06 \ cm[/tex]
I is the current passing through both the wire;
[tex]\rm I_1 = I_2 =I = 0.12 \ A[/tex]
The megnetic field strength at point a is found as;
[tex]\rm B_a = \frac{\mu_0 I_1}{2 \PI \ l_1 } - \frac{\mu_0 I_2}{2 \PI \ l_2 } \\\\ \rm B_a =\frac{\mu_0 }{2 \pi } [\frac{I_1}{L_1} - \frac{I_2}{L_2} ] \\\\ \rm B_a =\frac{4 \times 3.14\times 10^{-7} }{2 \pi } [\frac{12}{0.02} - \frac{12}{0.06} ] \\\\ \rm B_a =8 \times 10^{-5} \ T[/tex]
Hence the magnetic field strength at point a will be [tex]\rm B_a = 8 \times 10^{-5} \ T[/tex].
To learn more about the magnetic field strength refer to the link;
https://brainly.com/question/10638317
