How can we express the Lorentz force law in SI units?

AI Thread Summary
The discussion focuses on expressing the Lorentz force law, specifically the equation F = BIL sinΘ, in SI units. It clarifies that the unit of magnetic field B can be derived as N/C(m/s) or Ns/Cm, leading to the conclusion that the force F also equates to Newtons (N). The relationship between energy in joules and the units of amperes is explored, showing that the units cancel appropriately to confirm the equation's validity. Additionally, the breakdown of joules into mass and velocity units reinforces the consistency of the derived units. Overall, the conversion and relationships among the units affirm the expression of the Lorentz force law in SI units.
divyashree
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How do we say that F=BIL SINΘ using the SI units?:confused:
Newton(N)= Weber/m2 * ampere*meter.

please explain as soon as possible.:approve:
 
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Use magnetic lorentz force on a charged particle equation. And you can prove

F=BqvsinΘ.(Magnitude only).

so B= F/qvsinΘ
So, the unit of B is N/C(ms^(-1))

multiply s on both numerator and denominator,

so the unit is Ns/Cm

But F = BILsinΘ (Force on current carrying wire)

Unit of RHS is therefore

=(Ns/Cm)Am
Here A is ampere But A=Cs^(-1)

Substituting, you get the unit as N which is the unit of LHS
 
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A Weber is also energy in joules (stored in field) per ampere. So the amperes and numerator meter cancel and you are left with force (N) = energy (J) / length (m)...which is true since work is force times displacement. You could also break the Joule down into (mass * velocity squared) kg*m^2/s^2. Observe dividing a meter gives you the Newton (mass * acceleration) (kg*m/s^2).
 

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