Respuesta :
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 [tex]x_{1}=-2.2 cm[/tex]
Distance [tex]x_{2}=+2.2\ cm[/tex]
(A). We need to calculate the magnetic field
If the currents are in the same direction
The magnetic field is in both wires
[tex]B_{1}=B_{2}[/tex]
[tex]\dfrac{\mu_{0}I_{1}}{2\pi(r)}=\dfrac{\mu_{0}I_{2}}{2\pi(x-r)}[/tex]
Put the value into the formula
[tex]\dfrac{I_{1}}{(r)}=\dfrac{I_{2}}{4.4-r}[/tex]
Put the value into the formula
[tex]\dfrac{6.0}{r}=\dfrac{2.6}{4.4-r}[/tex]
[tex]x = \dfrac{6.0\times4.4}{8.6}[/tex]
[tex]x =3.0\ cm[/tex]
The point where the magnetic field is zero
[tex]x = 3.0-2.2 = 0.8\ cm[/tex]
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
[tex]B_{1}=B_{2}[/tex]
[tex]\dfrac{\mu_{0}I_{1}}{2\pi(r)}=\dfrac{\mu_{0}I_{2}}{2\pi(x+r)}[/tex]
Put the value into the formula
[tex]\dfrac{I_{1}}{(r)}=\dfrac{I_{2}}{4.4+r}[/tex]
Put the value into the formula
[tex]\dfrac{6.0}{r}=\dfrac{2.6}{4.4+r}[/tex]
[tex]x = \dfrac{6.0\times4.4}{3.4}[/tex]
[tex]x =7.76\ cm[/tex]
The point where the magnetic field is zero
[tex]x = 7.76-2.2 = 5.56\ cm[/tex]
The magnetic field is zero at 5.56 cm.
Hence, This is the required solution.
