Answer:
x= 0.077 m from the wire carrying 5.0 A current.
Explanation:
- If the wire can be approximated as an infinite one, and we can neglect the diameter of the wire, we can find the magnetic field B at a distance d from the wire, with the following expression:
[tex]B =\frac{\mu_{0} * I}{2*\pi*d}[/tex]
- Due to the currents are in the same direction, this means that the magnetic field lines (taking the shape of circumferences) will have opposite directions between the wires.
- So, if we assume that at some distance from both wires, the magnetic field will be 0, we can write the following equation:
[tex]\frac{\mu_{0} * I_{1}}{2*\pi*x} - \frac{\mu_{0} * I_{2} }{2*\pi*(d-x)} = 0[/tex]
- where I₁ = 5.0A, I₂= 8.0A and d = 0.2 m
- Simplifying common terms, we can solve for x, as follows:
[tex]\frac{I_{1} }{x} = \frac{I_{2} }{(d-x)} \\ \frac{5.0A}{x(m)} = \frac{8.0A}{(0.2m-x(m))}[/tex]
⇒ [tex]x =\frac{1m}{13} = 0.077 m = 7.7 cm[/tex]
