Let's Find Out Currents In The Arc Portion, Which Are In Parallel Across X and Y.
⇒ iABC = RADC = lADC = 60°
⇒iADC = RABC = lABC= 2π-60°
( Current Is Inversely Proportional To Resistance)
( Resistance Directly Proportional To Length)
(You Can Treat 60° as π/3)
( Note: 'i' is current, 'R' is Resistance, 'l' is Length)
Therefore, iABC = i × 60°/2π
iADC = i(2π-60°)/2π
BABC= Magnetic field due to arc portion ABC
= µº(i× 60°/2π)(2π-60°)/ 4πr
= µ°i×60°(2π-60°)/8π²r
Similarly, BADC= Magnetic Field Due To Arc ADC
= µ°[i(2π-60°)/2π]× 60°/4πr
= µ°i×60°(2π-60°)/8π²r
B1= BABC, B2= BADC
Hence B1/B2= 1
(Please Try To Formulate The Solution By Yourself In Notebook And Understand The Concept Because I Faced Some Problems In Writing It Properly.... Good Luck For Your Studies.......)