For a current element i , dl located at a position r , the magnetic field produced at the origin is

Step-by-step solution

According to the Biot-Savart law, the magnetic field d B at a position vector r ' due to a current element i , dl located at a position vector r is given by: d B = ₀ i 4 dl ( r ' - r ) | r ' - r |^3 Here, the magnetic field is to be evaluated at the origin, so r ' = 0 . Substituting r ' = 0 , we get: d B = ₀ i 4 dl ( 0 - r ) | 0 - r |^3 = ₀ i 4 dl (- r ) r^3 d B = - ₀ i 4 dl r r^3 Using the property of cross product, dl (- r ) = r dl . Therefore, the magnetic field can also be written as: d B = ₀ i 4 r dl r^3