Answer:
a) X = 0.767cm
b) X = 6.9cm
Explanation:
If both currents are in the same direction, the point of magnetic field zero must be somewhere in between the two wires. In this case, we have:
[tex]B =\frac{ \mu o*I}{2*\pi*d}[/tex] Since both magnetic fields must be equal in order cancel each other, and assuming that the point is closer to the 3A wire:
[tex]\frac{\mu o *6}{2*\pi*(2.3+x)*K_{cm}} = \frac{\mu o *3}{2*\pi*(2.3-x)*K_{cm}}[/tex] where [tex]K_{cm}[/tex] would be the factor to convert the distances from cm to m.
If we solve the equation for x, we get:
x = 0.767cm
Now, if both currents are in opposite direction, the point of magnetic field zero would be outside of the two wires and closer to the 3A wire. The formulas for this scenario would be:
[tex]\frac{\mu o *6}{2*\pi*(2.3+x)*K_{cm}} = \frac{\mu o *3}{2*\pi*(x-2.3)*K_{cm}}[/tex] where [tex]K_{cm}[/tex] would be the factor to convert the distances from cm to m.
If we solve the equation for x, we get:
x = 6.9cm
The points at the x-axis for which the magnetic field is zero if the two currents are in the same and opposite direction are mathematically given as
Question Parameter(s):
A long wire carrying a 6.0 A current perpendicular to the xy-plane
intersects the x-axis at x=−2.3cm.
A second, parallel wire carrying a 3.0 A current intersects the x-axis at x=+2.3cm.
Generally, the equation for the Magnetic field is mathematically given as
[tex]B =\frac{ \mu o*I}{2*\pi*d}[/tex]
Therefore
[tex]\frac{\mu o *6}{2*\pi*(2.3+x)*K} = \frac{\mu o *3}{2*\pi*(2.3-x)*K}[/tex]
x = 0.767cm
In conclusion, For opposite directions
[tex]\frac{\mu o *6}{2*\pi*(2.3+x)*K} = \frac{\mu o *3}{2*\pi*(x-2.3)*K}[/tex]
x' = 6.9cm
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