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

The magnetic field at P due to current elements PQ and PR is zero as the point P is on the conductor.
Therefore, the magnetic field at P due to current element QR is
`B=(mu_(0)I)/(4pi(PD))[ sin phi_(1)+ sin phi_(2)]`
`=(mu_(0)I)/(4pixx12x) [(((9x)/(5)))/(3x)+(((16x)/(5)))/(4x)]`
`=(mu_(0)Ixx5)/(48 pix) ((3)/(5)+(4)/(5))`
`=(7)/(48) (mu_(0)I)/(pi x)`