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Two long mutually perpendicular conducto...

Two long mutually perpendicular conductors carrying currents `I_1` and `I_2` lie in one plane, Find the locus of points at which the magnetic induction is zero.

Text Solution

Verified by Experts

The correct Answer is:
A, B
In first quadrant magnetic field ue to `I_1` is outwards and due to `I_2` is inwards. So, net magnetic field may be zero.
Similarly, in third quadrant magnetic field due to `I_1` is inwards and due to `I_2` magnetic fiedl is outwards. Hence only in first and third quadrants magnetic field may be zero.
Let magnetic field is zero at point P(xy) then
`B_(I_1)=B_(I_2)`
`:. mu_0/(2pi) I_1/y mu_0/(2pi) I_2/x`
`:. y=I_1/I_2x`
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Knowledge Check

  • Two mutually perpendicular conductors carrying currents I_(1) and I_(2) lie in one plane. Locus of the point at which the magnetic induction is zero, is a:

    A
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    B
    parabola with vertex as the point of intersection of the conductors
    C
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    D
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  • Two long straight conductors with corrents I_(1) and I_(2) are placed along X and Y axes. The equation of locus of points of zero magnetic induction is :

    A
    `Y = X`
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    `Y = (I_(1))/(I_(2))X`
    D
    `Y = (X)/(I_(1)I_(2))`

  • Two mutually perpendicular insulated long conducting wires carrying equal currents I, intersect at origin. Then the resultant magnetic induction at point P (2m, 3m) will be-

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    C
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    D
    0

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