A thick current carrying cable of radius 'R' carries current 'I' uniformly distributed across its cross section. The variation of magnetic field B(r) due to the cable with the distance 'r' from the axis of the cable is represented by :

In the product

$$\overrightarrow F = q\left( {\overrightarrow v \times \overrightarrow B } \right)$$

$$ = q\overrightarrow v \times \left( {B\widehat i + B\widehat j + {B_0}\widehat k} \right)$$

For q = 1 and $$\overrightarrow v = 2\widehat i + 4\widehat j + 6\widehat k$$ and $$\overrightarrow F = 4\widehat i - 20\widehat j + 12\widehat k$$

What will be the complete expression for $$\overrightarrow B $$ ?

A uniform conducting wire of length 12a and resistance 'R' is wound up as a current carrying coil in the shape of ,

(i) an equilateral tringle of side 'a'

(ii) A square of side 'a'

The magnetic dipole moments of the coil in each case respectively are :