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KittyGotham
15.10.2020 •
Physics
A long wire carrying a 5.5 A current perpendicular to the xy-plane intersects the x-axis at x=−2.0cm . A second, parallel wire carrying a 2.5 A current intersects the x-axis at x=+2.0cm . Part A At what point on the x-axis is the magnetic field zero if the two currents are in the same direction? Express your answer in centimeters. x x = nothing cm SubmitRequest Answer Part B At what point on the x-axis is the magnetic field zero if the two currents are in opposite directions? Express your answer in centimeters. x x = nothing cm SubmitRequest Answer Provide Feedback Next
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Ответ:
a
The point on the x-axis where the magnetic field will be zero is![d = 2.8 \ cm](/tpl/images/0806/9733/aedc7.png)
b
The point on the x-axis where the magnetic field will be zero is
Explanation:
From the question we are told that
The first current is![I_1 = 5.5 \ A](/tpl/images/0806/9733/6f438.png)
The point of x- axis intersection is![x = -2.0 \ cm](/tpl/images/0806/9733/7f7df.png)
The second current is![I_2 = 2.5 \ A](/tpl/images/0806/9733/ba99f.png)
The point of intersection of the x-axis is![x = 2 .0 \ cm](/tpl/images/0806/9733/54e0c.png)
Generally given that the current of the two wires are same direction it means that the magnetic field in -between the wires will cancel out giving zero
So
=>![B_1 = B_2](/tpl/images/0806/9733/3bb7d.png)
=>![\frac{\mu_o * I_1 }{2 * \pi * d } = \frac{\mu_o * I_2 }{2 * \pi * (4 -d) }](/tpl/images/0806/9733/19d63.png)
Here d is the of one wire to the point where the magnetic field is 0
and given that the total distance in-between the wire is D = 2 = 2 = 4
Hence the distance of the other wire to the point where magnetic field is zero is (4 - d)
So
=>![8d = 22](/tpl/images/0806/9733/53621.png)
=>![d = 2.8 \ cm](/tpl/images/0806/9733/aedc7.png)
So the point on the x-axis where the magnetic field will be zero is![d = 2.8](/tpl/images/0806/9733/f8634.png)
Generally given that the current of the two wires are opposition direction it means that the magnetic field at a position which is not in-between the wire will be zero
Let that position be k
Let the distance from the middle of both wires to k be Z
So
=>![5.5 Z - 11 = 5+ 2.5 Z](/tpl/images/0806/9733/e83e6.png)
=>![3Z = 16](/tpl/images/0806/9733/e3c9d.png)
=>![Z = 5.333\ cm](/tpl/images/0806/9733/5f590.png)
Ответ: