The magnetic field at the origin due to the current flowing in the wire is

Options

A. `mu_(0)/(4 pi) (i vec (dl) xx vec r)/r^(3)`
B. `- (mu_(0))/(4 pi) (i vec (dl) xx vec r)/r^(3)`
C. `- mu_(0)/(4 pi) (i vec (dl) xx vec r)/r^(3)`
D. `(mu_(0)i)/(4 pi) (vec r xx vec (dl))/r^(3) `

Answer

c, d

Explanation

In Biot-Savart law, position vector `vec r` is taken as a position vector of a point where field is to be calculated, with respect to current element.
So in this situation given `vec r` is opposite to that in Biot-Savart law. To compensate for the opposite direction of position vector, we can apply negative sign or can reverse the order of multiplication in Cross product. Hence options (c) and (d) are correct.