Find the magentic inducrtion at the centre of a recentagular wire frame whose diagonal is equal to `varphi = 30^(@)`, the current flowing in the frame equlas `I = 5.0 A`.

Explanation

We know that magnetic intuction due to a streight current carrying wire at any point, at a perpendiuclar distance from it is given by :
`B = (mu_(0) i)/(4pi r) (sin theta_(2) + sin theta_(2))`
where `r` is the perpendicular distnace of the wire from the point, considered, and `theta_(1)` is the angle between the line, joining the upper point of straight wire to the considered point and the perpendicular drawn to the wire and `theta_(2)` that from the lower point to the straight wire.
Hence, `E_(1) = B_(3) = (mu_(0))/(4pi) (i)/((d//2) "sin" (varphi)/(2)) {"cos" (varphi)/(2) + "cos" (varphi)/(2)}`
and `B_(2) = B_(4) = (mu_(0))/(4pi (i)/((d//2) "cos" (varphi)/(2))) ("sin" (varphi)/(2) + "sin" (varphi)/(2))`
Hence, the magnitude of total magnetic induction at `O`,
`B_(0) = B_(1) + B_(2) + B_(3) + B_(4)`
`= (mu_(0))/(4pi) (4i)/(d/2) [("cos" (varphi)/(2))/("sin" (varphi)/(2)) + ("sin" (varphi)/(2))/("cos" (varphi)/(2))]`