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)(I dl sin theta)/(r^(2))`
`dl = Delta x=10^(-2) m, I=10 A, r=0.5 m=y, mu_(0)//4pi=10^(-7)(TM) /(A)`
`theta=90^(@), sin theta=1`
`|dB|=(10^(-7)xx10xx10^(-2))/(25xx10^(-2))=4xx10^(-8)T`
The direction of the field is in the +z-direction. This is so since,
`dlxxr=Delta x hati xx y Delta x(hati xx hatj)y Delta x hatk`
We remind you of the following cyclic property of cross-products,
`hati xx hatj=k, hatj xx hatk= hati, hatkxx hati=hatj`
Note that the field is small in magnitude.