Two long parallel conductors I and II placed at right angles to a metre scale, at the 2 cm and 6 cm marks, as shown. They carry currents of 1 A and 3 A respectively in same direction. They will produce zero magnetic field at the

Options

A. Zero mark
B. 10 cm mark
C. 3 cm mark
D. 6 cm mark

Explanation

Current carrying wires are shown in the figure. In region 1 and 3 magnetic fields produced by both the conductors have same direction so they will add on.

In region 2, magnetic fields produced by both the conductors are not same, so there is possibility to get a point where net magnetic field is zero. Let Pbe the point where net magnetic field will be zero.
Here, XP = r and YP = (4 -r)
`l_1 = 1 A, l_(2) = 3 A`
Magnetic field produced by a current carrying conductor at a distance r from it,
`B = (mu_@ I)/(2 pi r)`
For conductor I, `B_i = (mu_@ l_1)/(2 pi r)`
For conductor II, `B_(II) = (mu_@ l_2)/((2pi(4-r))`
Net magnetic field at P is Zero, So, `B_I = B_II`
` (mu_0 l_1)/(2pi r) = (mu_@ l_2)/((2pi (4-r))`
`rArr (4-r) l_1 = l_2 r`
`rArr 1(4-r) = 3r`
`rArr = 4r = 4 therefore r =1 cm`
Position of the point P on the scale = 2 + 1 = 3 cm