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

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SUMMARY

The Lorentz force law can be expressed in SI units as F = BIL sin(θ), where F represents force in Newtons (N), B is the magnetic field in Weber per square meter (Wb/m²), I is current in Amperes (A), and L is length in meters (m). The unit of the magnetic field B can be derived as N/(C·m/s), which simplifies to N·s/(C·m). This confirms that the units on both sides of the equation are consistent, as energy in Joules (J) divided by length in meters (m) also yields force in Newtons (N). The relationship between these units illustrates the fundamental principles of electromagnetism.

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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
 
Last edited:
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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