A wire placed along north-south direction carries a current of 10 A from south to north. Find the magnetic field due to a 1 cm piece of wire at a point 200cm north-east from the piece.

Explanation

Solution:
figure 35.2
The situation is shown in figure(35.2). As the distance
of P from the wire is much larger than the length of the
wire, we can treat the wire as a small element. The
magnetic field is given by
` (vec(dB)) = ((mu_0)/4pi)i (((vec (dl) xx ( vec r))/ r^3)`
or, `dB=(mu_0/4pi)i ((dl sin theta)/r^2)`
`= (10^-7)(T mA^-1)(10A)(((10^-2 m)sin 45^@)/(2m ^2))`
`= 1.8 xx (10^-9) T.`
The direction of `(vec B) is the same as that of (vec dl) xx (vec r). From
the figure, it is vertically downward.