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 `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

`vecB_(R)=vecB` due to ring
`vecB_(1)=vecB`due to wire `-1`
`vecB_(2)=vecB`due to wire `-2`
In magnitudes `B_(1)=B_(2)=(mu_(0)I)/(2pir)` Resultant of `B_(1)` and `B_(2)=2B_(1) cos theta=(mu_(0)Ia)/(pir^(2))`
`B_(R)=(2mu_(0)Ipia^(2))/(4pir^(3))` For zero magnetic field at `P`
`(mu_(0)la)/(pir^(2))=(2mu_(0)Ipia^(2))/(4pir^(3)) rArrh~~1.2a`