Question

(a) calculate the amplitude (largest magnitude) and direction of the magnetic field produced by the two power lines at the base of the tower, when a current of 2 ✕ 104 a in the left power line is headed out of the page, and a current of 2 ✕ 104 a in the right power line is headed into the page. magnitude t direction

Answer 1

`1.74678 * 10^(-5)` T, up

Step-by-step explanation:

If the height of power line, h = 60 m and distance between the power lines, d = 16 m, then we can use Pythagorean theorem to find the distance from power lines to the base, R.

`R^2 = h^2+(d/2)^2\\\\R = √(h^2+(d/2)^2) = √(60^2+8^2) = 60.53` m

We need to find magnetic fields calculated from two current carrying wires and add them to find magnetic field at the base of the tower.

`I(t) = I_0sin(2\pi f t)\\B(t) = B_(out)+B_(in)\\B_(out)(t) = (\mu_0)/(4\pi) (2I_(out)(t))/(R) <cos\theta,sin\theta,0>\\B_(in)(t) = (\mu_0)/(4\pi) (2I_(in)(t))/(R) <-cos\theta,sin\theta,0>`

Then,

`B(t) = 2(\mu_0)/(4\pi) (2I(t))/(R)sin\theta` in +y direction

Hence,

`B = 2*(4\pi * 10^(-7))/(4\pi)*(2*2*10^4)/(60.53)*(8)/(60.53) = 0.0000174678 = 1.74678 * 10^(-5)` T

The direction is +y, that is, up.