We have the formula for a force acting on a current carrying conductor.
B = magnetic induction = magnetic field strength.
Force = B I L ie., current = I length = L force = newtons.
let dimensions of current be [ A ]
M L T⁻² = B A L
B = [ M T⁻² A⁻¹ ]
we have the formula for magnetic field strength at a point d distance away from a current carrying conductor as :
B = μ₀ I / (2 π d) this is found by Ampere's circuital law.
μ₀ = Newtons/Ampere²
B = M L T⁻² A⁻² * A L⁻¹ dimensions = M T⁻² A⁻¹ units = Tesla or kg / sec²-Amp or Newtons/Amp-meter