Question

Two long, parallel wires carry currents of 11 = 4.80 A and I2 = 1.80 A in opposite directions (see figure below). The wire 1 is placed at y = + 2.80 cm and wire 2 is at y = - 2.80 cm. Find the location on y-axis where the net magnetic field due to these two current carrying wires is zero. 2.1 cm

Two long, parallel wires carry currents of I₁ = 4.80 A and I₂ = 1.80 A in opposite directions (see figure below). The wire 1 is placed at y = + 2.80 cm and wire 2 is at y = - 2.80 cm. Find the location on y-axis where the net magnetic field due to these two current carrying wires is zero. ** my answer was wrong and I can't figure out how to correctly solve this**

Answer 1

Let us assume the magnetic field is zero at y=a. So, we need to find a.

The magnetic field at this point due to wire 1 is

$B_1=\frac{\mu_oI_1}{2\pi(a-y_1)}$

And the magnetic field due to wire 2 is

$B_2=\frac{\mu_o(-I_2)}{2\pi(a-y_2)}$

The sum of these two fields is zero. i.e

$B_1+B_2=0$

$\Rightarrow \frac{\mu_oI_1}{2\pi(a-y_1)}+\frac{\mu_o(-I_2)}{2\pi(a-y_2)}=0$

$\Rightarrow \frac{I_1}{a-y_1}=\frac{I_2}{a-y_2}$

Putting the values

$\Rightarrow \frac{4.8}{a-(+2.8)}=\frac{1.8}{a-(-2.8)}$

$\Rightarrow \frac{4.8}{a-2.8}=\frac{1.8}{a+2.8}$

$\Rightarrow 4.58a+13.44=1.8a-5.04$

$\Rightarrow 4.58a-1.8a=-5.04-13.44$

$\Rightarrow 2.78a=-18.48$

$\Rightarrow a=\frac{-18.48}{2.78}=-6.65\ cm$

So, the correct answer to this problem is -6.65 cm.