Match the following :

Explanation

The induction at C is

`vecB=vecB_(1)+vecB_(2)+vecB_(3)+vecB_(4)` …………. (i)
`vecB_(1)=(mu_(0)i)/(4piR)odot` ….(ii) `vec(B_(2))=(mu_(0)i_(1)theta_(1))/(4piR)` …(iii)
`vec(B_(3))=(mu_(0)i_(2)theta_(2))/(4piR)odot....(iv) vecB_(4)=0.....(v)`
Using the above equations, we get
`vecB=(mu_(0))/(4piR)(i+i_(3)theta_(2)-i_(1)theta_(1))odot` (a)
Since, the branches 2 and 3 are in parallel,
`i_(1)R_(1)=i_(2)R_(2)`
Since, `R_(1)=p(l_(1))/A=(p(Rtheta_1))/A` and `R_(2)=p/A(Rtheta_(2))`
`i_(1)theta_(1)=i_(2)theta_(2)` ....(b)
using equations (a) and (b ), we get
`B=(mu_(0)i)/(4piR)odot`