Find the magentic induction of the field at the pont `O` if a current-carrying wire has the shape shown in Figa,b,c The raidius of the curved part of the of the weir is `R` the linear parts are assumed to be very long.

Explanation

(a) From symmetry
`B_(0) = B_(1) + B_(2) + B_(3)`
`= 0 + (mu_(0))/(4pi) (i)/(R) pi + 0 = (mu_(0))/(4pi) (i)/(R)`
(b) From symmetry
`B_(0) = B_(1) + B_(2) + B_(3)`
`= (mu_(0))/(4pi) (i)/(R) + (mu_(0))/(2pi) (i)/(R) (3pi)/(2) + 0 = (mu_(0))/(4pi) (i)/(R) [1 + (3pi)/(2)]`
(c) From symmetry
`B_(0) = B_(1) + B_(2) + B_(3)`
`= (mu_(0))/(4pi) (i)/(R) + (mu_(0))/(4pi) (i)/(R) pi + (mu_(0))/(4pi) (i)/(R) = (mu_(0))/(4pi) (i)/(R) (2 + pi)`