A wire is bent into the shape shown in fig and the magnetic field is measured at `P_1` when the current in the wire is I. The same wire is then formed into the shape shown in the Fig and the magnetic field is measured at point `P_2` when the current is again I. If the total length of wire is the same in each case, what is the ratio of `B_1//B_2` ?

Explanation

Case I: `vecB_("net")=vecB_1+vecB_2+vecB_3`
`=[(mu_0I)/(4pil)[0+sin45^@]+(mu_0I)/(4pil)[sin45^@+sin45^@]`
`+(mu_0I)/(4pil)[0+sin45^@]]ox`

`:. |vecB_("net")|=(mu_0I)/(sqrt2pil)=B_1`
CaseII: `2pir=4l implies (2l)/pi`
Magnetic field at the centre of semicircle,
`B_("semicircle")=(mu_0I)/(4r)=(mu_0Ipi)/(8l)=B_2`
`(B_1)/(B_2)=(mu_0I)/(sqrt2pil)xx(8l)/(mu_0Ipi)=(4sqrt2)/(pi^2)`.