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

4.57 cm

Step-by-step explanation:

Magnetic field in a wire is given by:

`B=(\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=(\mu_0\cdot 2)/(2\pi x)`

`B_2=(\mu_0 \cdot 5)/(2\pi\cdot (16-x))`

`(\mu_0 \cdot 2)/(2\pi x)=(\mu_0 \cdot 5)/(2\pi\cdot (16-x))`

`(2)/(x)=(5)/(16-x)`

`x=(32)/(7)`