1.

Two long straight parallel wires A and B separated by a distance d, carry equal current I flowing in same direction as shown in the figure. (a) Find the magnetic field at a point P situated between them at a distance x from one wire. (b) Show graphically the variation of the magnetic field with distance x for 0 lt x lt d.

Answer»

Solution :(a) Magnetic field at POINT due to current I in wire A, `B_A= (mu_(0) I)/(2pi x) uparrow`
and magnetic field due to current I in wire B, `B_(B)=(mu_(0) I)/(2pi (d-x)) downarrow`
Net magnetic field `B=(B_(A)-B_(B)) uparrow =(mu_(0)I)/(2pi) [1/x-(1)/((d-x))] `
`rArr B=(mu_(0)I)/(2pi) (d-2pi)/(x(d-x)) uparrow`

(b) Variation of magnetic field B with DISTANCE x is shown here.
For `x=d/2` magnetic field B=0. For `x lt d/2` magnetic field B is directed UPWARD and for `x gt d/2` magnetic field B is directed downward.


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