Biot-Savart law indicates that the moving electrons (velocity `vecv` ) produce a magnetic field `vecB` such that

Options

A. `B bot v`
B. `B || v`
C. it obeys the inverse cube law.
D. it is along the line joining the electron and point of observation.

Answer

A

Explanation

For a current carrying small element `vec (dl)` carrying a current I, the magnetic field at a distance r from it is given by the Biot-Savart law.
According to the Biot - Savart law,
`vecB = mu_(0)/(4 pi) (Ivec(dl) xx vec r)/r^(3)`
Also, `I = q//dt`
where, q = charge flowing through the element dt = time taken by charge q to flow.
`:. vecB = mu_(0)/(4 pi) (q/(dt)(vecdl)xx vecr)/r^(3) = mu_(0)/(4 pi) (q[vec(dl)/(dt)] xx vec r)/r^(3)`
`= mu_(0)/(4 pi) (q(vec v xxvecr))/r^(3) " " [(dl)/(dt) = v]`
where v = velocity of charge q
` :. " " B = mu_(0)/(4 pi) (q(vec v xx vec r))/r^(3) ` ...(i)
So, from(i), we can conclude that `vec B` is perpendicular to the plane containing `vec v " and vec r`.
Also, `vec B` at a point obeys the inverge square law.
So, option (a) is correct.