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Solution :

Let us first find out currents in the arc portions, which are in parallel across points X and Y <br> `rArr (i_(XAY))/(i_(XBY)) = (R_(XBY))/(R_(XAY)) = (l_(XBY))/(l_(XAY)) = (theta )/(2pi - theta)` <br> (Here i, R and l represent current, resistance and length respectively) <br> Therefore, <br> `i_(XAY) = (itheta)/(2pi), i_(XBY) = (i(2pi - theta))/(2pi)` <br> `rArr B_(XAY)=` Magnetic field due to arc portion XAY <br> `= (mu_(0) ((itheta)/(2pi)) (2pi - theta))/(4pi r) ox = (mu_(0) i theta (2pi - theta))/(8pi^(2) r) ox` <br> and `B_(XBY) = (mu_(0)[(i(2pi - theta))/(2pi)] theta)/(4pi r) o. = (mu_(0) itheta(2pi - theta))/(8pi^(2) r) o.` <br> Net Magnetic field `= vecB_(XAY)^(•) + vec(B)_(XBY) = 0` at O <br> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/AAK_T6_PHY_C17_SLV_035_S01.png" width="80%">