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Find the magnetic field induction at a p...

Find the magnetic field induction at a point O if the wire carrying current `I=8*0A` has a shape as shown in figure. The radius of the curved path of the other wire is `r=100mm` and linear paths of wire are very long.

Text Solution

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Total magnetic field induction at O due to current through the parts 1, 2 and 3 will be
`vecB=vecB_1+vecB_2+vecB_3`
`=(mu_0)/(4pi)[I/r(-hatk)+(Ipi)/(r)(-hati)+I/r(-hatk)]`
`=-(mu_0)/(4pi)I/r(2hatk+pihati)`
`:. |vecB|=(mu_0)/(4pi)I/r(sqrt(2^2+pi^2))`
`=10^-7xx(8)/((100xx10^-3))sqrt(4+(22//7)^2)`
`=2*98xx10^-5T`
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