An element `dvecl=dxhati` (where `dx=1cm`) is placed at the origin and carries a large current `i=10A`. What is the magnetic field on the Y-axis at a distance of `0.5m`?

Explanation

`|dB| = (mu_(0))/(4pi) (Idl sin theta)/(r^(2))`[ using eq.]
`dl = Deltax = 10^(-2)m, I = 10A, r = 0.5m = y. mu_(0)//4pi = 10^(-7) (Tm)/(A)`
`theta = 90^(@), sin theta = 1`
`|dB| = (10^(-7) xx 10 xx 10^(-2))/(25 xx 10^(-2)) = 4 xx 10^(-8)T`
The direction of the field is in the `+z`-direction. This is so since,
`dl xx r = Deltax hati xx y hatj = y Deltax (hati xx hatj) = y Delta x hatk`
We remind you of the following cyclic property of cross-products.
`hati xx hatj = hatk, hatj xx hatk = hati, hatk xx hati = hatj`
Note that the field is small in magnitude.