1.

A long wire bent as shown in fig. carries current I. If the radius of the semicircular portion is a, the magnetic field at centre C is A. `(mu_0I)/(4r)`B. `(mu_0I)/(4pir)sqrt(pi^2+4)`C. `(mu_0I)/(4pi)+(mu_0I)/(2pir)`D. `(mu_0I)/(4pir)sqrt(pi^2-4)`

Answer» Correct Answer - B
Total magnetic field induction at P is
`vecB=vecB_(ab)+vecB_(bc)+vecB_(cd)`
`=(mu_0)/(4pi)I/r(-hatj)+(mu_0)/(4pi)(piI)/(r)(-hatk)+(mu_0)/(4pi)I/r(-hatj)`
`=(mu_0)/(4pi)(2I)/(r)(-hatj)+(mu_0)/(4pi)(piI)/(r)(-hatk)`
`:. |vecB|=[((mu_0)/(4pi)(2I)/(r))^2+((mu_0)/(4pi)(piI)/(r))^2]^(1//2)`
`=(mu_0)/(4pi)I/rsqrt(4+pi^2)`


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