Question

Migratory birds use Earth’s magnetic field to guide them. Some people are concerned that human-caused magnetic fields could interfere with bird navigation. Suppose that a pair of parallel high-voltage lines, each carrying a current of 100A are 3.00 meters apart and lie in the same horizontal plane. Find the magnitude and direction of the magnetic field the lines produce at a point 15.0 m above the midpoint between the two lines in each of these two cases:

Answer 1

The direction of current is into the page.

The magnetic field
`$B_1$` due to the wire is perpendicular to AP and the magnetic field
`$B_2$` due to the wire is perpendicular to BP. Thus, the net magnetic field at point P is towards the right.

The net magnetic field at point P is

`$B_(net) = B_1 \cos \theta + B_2 \cos \theta$`

The magnetic field is

`$B_1=B_2=(\mu_0I)/(2 \pi L)$`

The angle θ is

`$\theta = \cos^(-1)(h)/(L)$`

The net magnetic field at point P is

`$B_(net)=\left((\mu_0I)/(2 \pi L)\right)\left((h)/(L)\right)+\left((\mu_0I)/(2 \pi L)\right)\left((h)/(L)\right)$`

`$=(\mu_0 Ih)/(\pi L^2)$`

a). The direction of the current for both the wires is from north to south. The net magnetic field is towards the right when we are facing south.

`$B_(net)=(\mu_0 Ih)/(\pi L^2)$`

`$=(\mu_0I L)/(\pi \left(√(h^2+(d/2)^2\right)^2))$`

`$=(4 \pi * 10^(-7) * 100 * 15)/(\pi \left(√(15^2+(3/2)^2\right)^2))$`

`$=2.64 * 10^(-6) \ T$`

The direction is towards the west.

b). Since, both the magnetic field are equal and opposite, so no magnetic field is produced.