A steady current `I` goes through a wire loop `PQR` having shape of a right angle triangle with `PQ = 3x, PR = 4x and QR = 5x`. If the magnitude of the magnetic field at `P` due to this loop is `k((mu_(0)I)/(48 pi x))`, find the value of `K`.

Answer

7

Explanation

Magnetic field at point P due to wires RP and PQ is zero. Only wire QR will produce magnetic field at P.
`r=3xxcos 37^(@)=(3x)(4/5)=(12x)/5`
Now `B=(mu_(0))/(4pi) I/(12x//5)[sin 37^(@)+sin 53^(@)]=7((mu_(0)I)/(48pix))`