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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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Similar questions

Q. Two long parallel wires A and B separated by a distance d, carry currents

i_{1}

i_{2}

respectively in the same direction. Write the following steps in a sequential order to find the magnitude of the resultant magnetic field at a point 'P', which is between the wires and is a distance '

x

' from the wire A.
(All the physical quantities are measured in SI units)
(a) Note the given values of

i_{1}, i_{2}

d

x

.
(b) Write the formula to find the magnetic field due to a long straight current carrying wire i.e.

B = \frac{μ_{0} i}{2 π r}

(c) Find the directions of the magnetic field at 'P' due to two wires A and B, using right hand thumb rule.
(d) Determine the magnetic field at P due to wire A, using

B_{1} = \frac{μ_{0} i_{1}}{2 π x}

(e) If the directions of magnetic field are same, then the resultant magnitude is equal to the sum of

B_{1}

B_{2}

.
(f) Determine the magnetic field

B_{2}

due to wire B at point P, ie.

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

(g) If the directions of magnetic fields are opposite to each other, then the resultant magnitude is equal to the difference of

B_{1}

B_{2}

.

Q. Two long, straight wires, each carrying a current of 5 A, are placed along the x- and y-axis respectively. The currents point along the positive directions of the axes. Find the magnetic fields at the points (a) (1 m, 1 m), (b) (−1 m, 1 m), (c) (−1 m, −1 m) and (d) (1 m, −1 m).

Q. Two long wires one carrying current 1 A and other carrying 2 A in the same direction are placed parallel to each other produces a net magnetic field B at the mid-point. What will be the field at mid-point when current 1 A is switched off?

Q. Two very long, straight, and insulated wires are kept at

90 °

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