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Two infinitely long current carrying conductors X and Y are kept parallel to each other, 24 cm apart in vacuum. They carry currents of 5 A and 7 A respectively, in the same direction, as shown in figure below. Find the position of a neutral point, i.e., a point where resultant magnetic flux density is zero. (Ignore earth.s magnetic field). 
 

Text Solution

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Consider that magnetic field density at point P is zero due to current carrying conductors.

According to right hand palm rule number 1, direction of magnetic field will be perpendicular to the plane of the paper.
(1) Downward due to current flowing in conductor X
(2) Upward due to current flowing in conductor Y
Since at point `P, B = 0`
`therefore B_1 = B_2`
`(mu_0)/(2pi) (I_1)/(x) = (mu_0)/(2pi)(I_2)/((24 - x))`
`5/x = 7/(24 - x)`
`5(24 - x) = 7x`
`5 xx 24 = 12 x`
`implies x= 10 ` cm from conductor X.
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