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Find the total magnetic induction at poi...

Find the total magnetic induction at point O due to current through curved portion and straight portion in the figure.

Text Solution

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`B_0=B_(CFE)+B_(CDE)` , `B_(CFE)=(mu_0)/(4pi)I/r(2pi-2phi)`
and `B_(CDE)=(mu_0)/(4pi)(I)/(OD)[sin phi+sin phi]=(mu_0Ixx2sinphi)/(4pixxrcosphi)=(mu_0I)/(4pi)2tanphi` `[:' OD=r cos phi]`
`:. B_0=(mu_0)/(4pi)I/r(2pi-2phi)+(mu_0I)/(4pir)xx2tanphi=(mu_0)/(2pir)[pi-phi+tanphi]`
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