In the given figure find out magnetic field at point B (Given : I=2.5A, r=5cm)

Options

A. `pi xx[1+(1)/(pi)] xx 10^(-5)T`
B. `pi[1+(1)/(pi)]xx10^(-6)T`
C. `pi((pi+1)/(pi))xx10^(-6)T`
D. `((pi+1)/(pi))xx10^(-6)T`

Answer

A

Explanation

`vecB_(B) =vecB_("wire")+vecB_("Ring")`
`vecB_("wire") =(mu_(0)i)/(4pi r)-(-hatk)+(mu_(0)i)/(4pi r)(-hatk)=(mu_(0)i)/(2pi r)(-hatk)`
`vecB_("Ring") =((mu_(0)i)/(2pi r)+(mu_(0)i)/(2r))-hatk`
`B_(B)=(mu_(0)i)/(2r) [(1)/(pi)+1]=(4pi xx 10^(-7)xx2.5)/(2xx5xx10^(-2))[1+(1)/(pi)]`
`=10pi xx 10^(-6) [1+(1)/(pi)] = pi xx [1 +(1)/(pi)] xx 10^(-5)T`