Answer:
The current of the outer coil is [tex]I_o = 3.99 \ A[/tex]
Explanation:
From the question we are told that
The number of turns of the inner coil is [tex]N_i = 170 \ turn[/tex]
The radius of the inner coil is [tex]R_i = 0.012 \ m[/tex]
The current of the inner coil is [tex]I_i = 6.2 \ A[/tex]
The number of turns of the outer coil is [tex]N_o = 220 \ turns[/tex]
The radius of the outer coil is [tex]R_o = 0.02 0 \ m[/tex]
Generally the net magnetic field is mathematically represented as
[tex]B = \frac{N \ mu I }{ 2 * R }[/tex]
Now from told that the net magnetic field is common
So
[tex]\frac{N_i \mu I_i} {2 * R _i} = \frac{N_o \mu I_o} {2 * R _o}[/tex]
Here [tex]\mu[/tex] is the permeability of free space
making [tex]I_o[/tex] the subject
[tex]I_o = \frac{ N_i I_i *2 * R _o}{N_o *2 * R _i}[/tex]
substituting values
[tex]I_o = \frac{ 170 *6.2 *2 * 0.020}{220 *2 * 0.012}[/tex]
[tex]I_o = 3.99 \ A[/tex]
