Question

Two long parallel wires 20 cm apart carry currents of 5.0 A and 8.0 A in the same direction. Is there any point between the two wires where the magnetic field is zero?

Answer 1

x= 0.077 m from the wire carrying 5.0 A current.

Step-by-step 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:

`B =(\mu_(0) * I)/(2*\pi*d)`

• 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:

`(\mu_(0) * I_(1))/(2*\pi*x) - (\mu_(0) * I_(2) )/(2*\pi*(d-x)) = 0`

• where I₁ = 5.0A, I₂= 8.0A and d = 0.2 m
• Simplifying common terms, we can solve for x, as follows:

`(I_(1) )/(x) = (I_(2) )/((d-x)) \\ (5.0A)/(x(m)) = (8.0A)/((0.2m-x(m)))`

⇒
`x =(1m)/(13) = 0.077 m = 7.7 cm`