A straight wire of length `pi //2` m is bent into a circular shape.O is the center of the circle so formed and P is a point on its axis which is at a distance 3 times the from O .A current of 1A is passed through it Calculate the magnitude of the magnetic field at the points O and P .

Explanation

Given : Circumference `C=pi/2` m
I =IA n=1
Circumference of a circle =`2pir`
`cancelpi/2=2cancelpir rArr r=1/4m`
r=0.25 m
We known that `B=(mu_0 2 pi n Ir^2)/(4pi(r^2+x^2)^(3//2))`
At `theta` , x=0
`B=(mu_02pinIr^(cancel2))/(4pir^(cancel31))`
`B=(mu_02pinI)/(4pir)=mu_0/(4pi)(2pinI)/(r)=10^(-7)xx(2xx3.14xx1xx1)/0.25`
`B=25.12xx10^(-7)` T
At `Px=3r=3xx0.25=0.75`
`B=mu_0/(4pi)(2pinIr^2)/((r^2+x^2)^(3//2))=10^(-7)xx(2xx3.14xx1xx1xx(0.25)^2)/([(0.25)^2 +(0.75)^2]^(3//2))`
`B=(0.3925xx10^(-7))/([0.062+0.562]^(3//2))=(0.3925xx10^(-7))/((0.624)^(3//2)) = (0.3925xx10^(-7))/((0.624)sqrt(0.625))=(0.3925xx10^(-7))/0.4933`
`B=0.795xx10^(-7)` T.