(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

four parallel infinite wires are arranged as shown in the figure: (see attachment)

a) calculate the value of the magnetic field produced along the central axis of the configuration (magnitude and direction)

b) a fifth wires is placed along a central axis, parallel to the four wires and equidistant from all four. if a current I_2 is sent through this wire, what is the force per unit length on the fifth wire?

c) if one wished to used the four outer wires to magnetically levitate the fifth central wire, what would be the relation between the linear mass density of the central wire (mass/length) and the currents I and I_2? also, in which direction would I_2 have to flow for the levitation to be possible? assume gravity acts downward, towards the bottom of the page, in the end-on view shown (see attachment).

2. Relevant equations

magnetic field, ampere's law, B = mu_0(I)/2pi(r) where mu_0 is constant = 4pi*10^-7, I is current, r is radius

magnetic field, biot-savart law, B = mu_0/4pi[integral(IdL/r^2)], where dL is change in length

force F = IL X B where x indicates cross product, L is length, I is current, B is net magnetic field

3. The attempt at a solution

part a, use amperes law to find the magnetic field from each wire at the center of the square formed by the four wires. where r is the center, so r = sqrt((a/2)^2 + (a/2^2).

how will i factor in the directions of the current flow, wouldn't they cancel each other out, such that the net magnetic field at the center would be B = 0? or do i just take the magnitude(absolute value)?

part b, use force equation and use net magnetic field from part a for B, use I = I_2, and L as constant to find force/unit length on fifth wire.

part c, i am lost here, ideas/tips appreciated. were my attempt for part a and b along the right lines?

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# Parallel infinite wires - magnetic field

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