An infinite conducting wire, which is bent in the shape of a hairpin (the curved part being a semicircle of radius` a = 1cm` ) as shown in the figure, carries a unit current

An infinite conducting wire, which is bent in the shape of a hairpin (the curved part being a semicircle of radius` a = 1cm` ) as shown in the figure,

Problem: An infinite conducting wire, which is bent in the shape of a hairpin (the curved part being a semicircle of radius` a = 1cm` ) as shown in the figure, carries a unit current

(A) 1.3 gauss    (B) 7.1 gauss     (C) 0.82 gauss    (d)0.51 gaus

Answer:

The magnetic field at the point P is due to the sum of 2 half-infinity conducting wires and half of the circular loop.

The magnetic field at P due one half-infinite wire is given by 

`B_(oo)=(mu_0I)/(4pia)(sin90^circ+sin0^circ)`T

`B_(oo)=10^-7/(10^-2)`T

`B_oo=10^-5`T

The magnetic filed at P due to half circle is 

`B_"cir"=1/2(mu_0I)/(2a)=3.14xx10^-5`T

The total magnetic field at P is 

`B=2xxB_(oo)+B_"cir"`

`B=2xx10^-5+3.14xx10^-5`T

`B=5.14xx10^-5`T

`B=0.514`G

Option D is correct.

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