To solve this problem, we need to determine the net current [tex]\( I \)[/tex] passing through a surface bounded by a closed path as given by Ampere's law:
[tex]\[
\sum B_1 \Delta \ell = \mu_0 I
\][/tex]
Here, [tex]\( I \)[/tex] represents the net current enclosed by the closed path. We are provided with the following individual currents:
7 A, 0 A, 12 A, 2 A, and 5 A.
Ampere's law essentially states that the magnetic field along a closed loop is proportional to the net current passing through the surface enclosed by the loop. To find the value of [tex]\( I \)[/tex], we sum up all the given currents:
[tex]\[
I = 7 \, \text{A} + 0 \, \text{A} + 12 \, \text{A} + 2 \, \text{A} + 5 \, \text{A}
\][/tex]
Adding these values:
[tex]\[
I = 7 + 0 + 12 + 2 + 5
\][/tex]
Performing the addition step-by-step:
[tex]\[
7 + 0 = 7
\][/tex]
[tex]\[
7 + 12 = 19
\][/tex]
[tex]\[
19 + 2 = 21
\][/tex]
[tex]\[
21 + 5 = 26
\][/tex]
Thus, the total net current [tex]\( I \)[/tex] passing through the closed path is:
[tex]\[
I = 26 \, \text{A}
\][/tex]
Therefore, according to Ampere's law, the value of [tex]\( I \)[/tex] on the right side of the equation is [tex]\( 26 \, \text{A} \)[/tex].
