Question

A long wire carrying a 6.0 A current perpendicular to the xy-plane intersects the x-axis at x=−2.2cm. A second, parallel wire carrying a 2.6 A current intersects the x-axis at x=+2.2cm. Part A. At what point on the x-axis is the magnetic field zero if the two currents are in the same direction?
Part B. At what point on the x-axis is the magnetic field zero if the two currents are in opposite directions?

Answer 1

Answer:

(A). The magnetic field is zero at 0.8 cm.

(B). The magnetic field is zero at 5.56 cm.

Explanation:

Given that,

Current in first wire I = 6.0 A

Current in second wire = 2.6 A

Distance $x_{1}=-2.2 cm$

Distance $x_{2}=+2.2\ cm$

(A). We need to calculate the magnetic field

If the currents are in the same direction

The magnetic field is in both wires

$B_{1}=B_{2}$

$\dfrac{\mu_{0}I_{1}}{2\pi(r)}=\dfrac{\mu_{0}I_{2}}{2\pi(x-r)}$

Put the value into the formula

$\dfrac{I_{1}}{(r)}=\dfrac{I_{2}}{4.4-r}$

Put the value into the formula

$\dfrac{6.0}{r}=\dfrac{2.6}{4.4-r}$

$x = \dfrac{6.0\times4.4}{8.6}$

$x =3.0\ cm$

The point where the magnetic field is zero

$x = 3.0-2.2 = 0.8\ cm$

The magnetic field is zero at 0.8 cm.

(B). We need to calculate the point where the magnetic field zero

If the currents are in the opposite direction

The magnetic field is in both wires

$B_{1}=B_{2}$

$\dfrac{\mu_{0}I_{1}}{2\pi(r)}=\dfrac{\mu_{0}I_{2}}{2\pi(x+r)}$

Put the value into the formula

$\dfrac{I_{1}}{(r)}=\dfrac{I_{2}}{4.4+r}$

Put the value into the formula

$\dfrac{6.0}{r}=\dfrac{2.6}{4.4+r}$

$x = \dfrac{6.0\times4.4}{3.4}$

$x =7.76\ cm$

The point where the magnetic field is zero

$x = 7.76-2.2 = 5.56\ cm$

The magnetic field is zero at 5.56 cm.

Hence, This is the required solution.