Electricity and Magnetism

28–188 Electricity and Magnetism

I d~s The product I d~s is the current element. Strictly speaking, I is the magnitude

of the [positive] current. Its direction is incorporated into d~s.

~r = r ˆr Both the magnitude, r, and the direction, ˆr, of the relative position of the

field point with respect to the current element affect the magnitude and direction of the

differential magnetic field. In particular, the magnitude falls off in proportion to

the squared distance.

I d~s × ˆr The differential contribution to the magnetic field at P lies orthogonal to the

plane formed by the current element d~s

i

and the displacement vector leading from the

current element