Why do the E-field and B-field have different units?

[tiredryan]

Note this is more of a coursework theory question then a specific homework question.

I am learning about E and B fields and electromagnetic waves. A common EM figure I find is the propagation of a photon where the E and B field propagate through space as seen in the following link.
http://www.astronomynotes.com/light/emanim.gif
The confusing thing is that the E field has different units than the B field where E = cB. Is there a physical meaning to this or should I just accept the equation as it is? I am guessing it falls out of Maxwell's equations, but it feels odd that an E and B field have different units when things like the units of force and pressure don't change.

Homework Statement

Why do the E-field and B-field have different units?

Homework Equations

E = cB
F = q(E + v x B)

The Attempt at a Solution

 

[RoyalCat]

The Magnetic Force on a moving particle is proportional to its velocity. If you wish to use q \vec v \times \vec B to describe the force, then obviously you can't have the same units for E and B.
There are, however, different systems of measurement where E and B -do- have the same units. One such system is the CGS system. In that system, the Lorentz Force is: q(\vec E+\frac{\vec v}{c} \times \vec B) and there E and B do have the same units.

 

[tiredryan]

Thanks for your response. Can you explain how the CGS works to an introductory physics student? How does E remain the same, but B changes by a factor of distance/time in a different unit system? When I think of feet and meters, they scale by a dimensionless constant. Similarly pressure can be expressed in Pa, torr, and bar and the only difference is a dimensionless constant scaling factor. Is there some unit system where length and pressure has the same units? How does CGS work differently?

The Magnetic Force on a moving particle is proportional to its velocity. If you wish to use q \vec v \times \vec B to describe the force, then obviously you can't have the same units for E and B.
There are, however, different systems of measurement where E and B -do- have the same units. One such system is the CGS system. In that system, the Lorentz Force is: q(\vec E+\frac{\vec v}{c} \times \vec B) and there E and B do have the same units.