Force on a Current
F = force, I = current, l = length of conductor, B = magnetic field, θ = angle between line of action of magnetic field and current
The first equation gives the force on a infinitesimal length d l of conductor. Assuming a straight conductor of length l , this reduces to the second equation.
University Physics, F W Sears, M W Zemansky, 3rd edition, Addison-Wesley, 1967