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Magnetic Field Due to Finite Wire

A long, strai...

Question

A long, straight wire carries a current along the z-axis, One can find two points in the x−y plane such that
(a) the magnetic fields are equal
(b) the directions of the magnetic fields are the same
(c) the magnitudes of the magnetic fields are equal
(d) the field at one point is opposite to that at the other point.

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Solution

(b) the directions of the magnetic fields are the same
(c) the magnitudes of the magnetic fields are equal
(d) the field at one point is opposite to that at the other point.
Consider a current carrying wire lying along x axis.
At any two points on z axis which are at equal distance from the wire,one above the wire and one below the wire,the magnitude of magnetic field will be same and their directions will be opposite to each other.
At any two points on z axis which are at different distances from the wire,one above the wire and other also above the wire,the magnitude of magnetic field will be different and their directions will be same to each other.

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i_{1}

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B = \frac{μ_{0} i}{2 π r}

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(d) Determine the magnetic field at P due to wire A, using

B_{1} = \frac{μ_{0} i_{1}}{2 π x}

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B_{2}

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B_{2} = \frac{μ_{o} i_{2}}{2 π (d - x)}

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