Question

Two long, straight wires both carry current to the right, are parallel, and are 16 cm apart. Wire one carries a current of 2.0 A and wire two carries a current of 5.0 A. How far from wire 1 is the net magnetic field equal to 0?

Answer 1

Answer:

4.57 cm

Explanation:

Magnetic field in a wire is given by:

$B=\frac{\mu_0 I}{2\pi r}$

Lets suppose the distance from wire 1 is $x$ where $\sum B=0$

$\sum B=0=B_1 - B_2$   where $B_1$ and $B_2$ are magnetic fields due to wire 1 and 2 at x since both fields are in opposite direction

$B_1=\frac{\mu_0\cdot 2}{2\pi x}$

$B_2=\frac{\mu_0 \cdot 5}{2\pi\cdot (16-x)}$

$\frac{\mu_0 \cdot 2}{2\pi x}=\frac{\mu_0 \cdot 5}{2\pi\cdot (16-x)}$

$\frac{2}{x}=\frac{5}{16-x}$

$x=\frac{32}{7}$