A current `I = 5.0 A` A flows along a thin wire shaped as shwon in Fig. The radius of a curved part of the wire is equal to `R = 120 mm`, the angle `2varphi = 90^(@)`. Find the magentic induction of the field at the point `O`.

Explanation

Magnetic induction due to the are segment at `O`,
`B_(are) = (mu_(0))/(4pi) (i)/(R) (2pi - 2 varphi)`
and magentic induction due to the line segment at `O`,
`B_(line) = (mu_(0))/(4pi R) (i)/(cos varphi) [2sin varphi]`
So, total magnetic induction at `O`,
`B_(0) = B_(are) + B_(line) = (mu_(0))/(2pi) (i)/(R) [pi - varphi + tan varphi] = 28 mu T`