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 wire2 is the direction PQ and RS, 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

`B_(R)=B` due to ring `B_(1)=B` due to wire 1 `implies B_(2)=B` due to wire 2
In magnitudes `B_(1)=B_(2)=(mu_(0)I)/(2pir)` Resultant of `B_(1)` and `B_(2) b=2B_(1)cos theta=2((mu_(0)I)/(2pi))(h/4)=(mu_(0)In)/(pir^(2))`
`B_(R)=(mu_(0)IR^(2))/(2(R^(2)+x^(2))^(3//2))=(2mu_(0)I pi a^(2))/(4pi r^(3))` As `R=a,x=h` and `a^(2)+h^(2)=r^(2)`
For zero magnetic field at P `(mu_(0)Ih)/(pir^(2))=(2mu_(0)Ipia^(2))/(4pir^(3))impliespia^(2)=2rhimpliesh~~1.2a`