The figure shows a circular loop of radius `a` with two long parallel wires `(numbered 1 and 2)` all in the plane of the paper . The distance of each wire from the centre of the loop is `d`. The loop and the wire are carrying the same current `I`. The current in the loop is in the counterclockwise direction if seen from above.
(q) The magnetic fields(B) at `P` due to the currents in the wires are in opposite directions.
(r) There is no magnetic field at `P`.
(s) The wires repel each other.

(4) When `d~~a` but wires are not touching the loop , it is found that the net magnetic field on the axis of the loop . In that case

Options

A. current in wire 1 and wire 2 is the direction PQ and SR, respectively and `h~~a`
B. current in wire 1 and wire 2 is the direction PQ and SR, respectively and `h~~a`
C. current in wire 1 and wire 2 is the direction PQ and SR, respectively and `h~~1.2a`
D. current in wire 1 and wire 2 is the direction PQ and RS, respectively and `h~~1.2a`

Answer

C

Explanation

(c) The net magnetic field at the given point will be zero if.
`|vecB_("wires")|=|vecB_("loops")|`
The direction of magnetic field at the given point due to the loop
is normally out of the plane. Therefore, the net magnetic field
due the both wires should be into the plane. For this current in
wire I should be along PQ and that in wire RS should be along SR.
`B_("loop")=(mu_0)/2 (ia^2)/((h^2+a^2)^(3//2))`
`B_("wires")=2xx(mu_0i)/(2pisqrt(d^2+h^2)) cos theta`

`:. (mu_0)/2. (ia^2)/((h^2+a^2)^(3//2)) =(2mu_0i)/(2pi) d/(d^2+h^2)`
`implies (a^2)/(2(h^2+a^2)^(3//2))=a/(pi(a^2+h^2)) implies pia=2sqrt(h^2+a^2)`
`implies a=(2h)/(sqrt(pi^2-4)) implies h~= 1.2a`