An element `Delta l = Delta x hat i` is placed at the origin and carries a large current I= 10 A( figure). What is the magnetic field on the y - axis at a distance of 0.5 m. `Delta x = 1` cm

Explanation

`|dB| = (mu_0)/(4pi) (Id // sin theta)/(r^2)`
`dl = Delta r = 10^(2) m , I =10 a, r=0.5 x =y`
`= 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= Delta x hat i xx hat j = y Deltax (hatixx hat j )= y Delta x hat k ( hat i xx hat j= hat k, hat j xx hatk = hati , hatk xx hati = hatj)`