Figure here shows three cases, in all cases the circular path has radius r and straight ones are infinitely long. For same current, the magnetic field at the centre P in cases 1, 2 and 3 have the ratio

Options

A. `(-pi/2):(pi/2):((3pi)/4-1/2)`
B. `(-pi/2+1):(pi/2+1):((3pi)/4+1/2)`
C. `(-pi/2):(pi/2):((3pi)/4)`
D. `(-pi/2-1):(pi/2-1/4):((3pi)/4+1/2)`

Answer

A

Explanation

(a) `vecB_1=(mu_0I)/(4r)odot, vecB_2=(mu_0I)/(4r)ox`
`vecB_3=(mu_0I)/(2r) (3/4)ox+(mu_0I)/(4pir)odot=(mu_0I)/(4r)[3/2ox+1/piodot]`
`=(mu_0I)/(4r)[(3pi-2)/(2pi)]ox=(mu_0I)/(4r)(2/pi)((3pi)/4-1/2)ox`
`B_1:B_2:B_3=-(pi/2):(pi/2):((3pi)/4-1/2)`