1 coulomb is 1 ampere per second and 1 ampere is 1 coulomb per second therefore they are always equivalent. They would only be different if you changed the time but the units themselves are based only on the current/charge in 1 second. So how come their SI definition is not the same?
[Physics] Are the Amp and coulomb equivalent
chargeelectric-currentelectricityunits
Related Solutions
The key difference is the $ \frac{1}{4\pi\epsilon_0} $, with $ \epsilon_0 $ in the SI formulation of charge, being vaccuum permittivity with units $ (charge)^2(time)^2 (mass)^{−1}(length)^{−3} $. This satisfies the unit cancellation, and in the SI system makes the electric constant $ \mu_0 $ and $ \epsilon_0 $ now derived units. (See Vacuum Permittivity or SI Unit Redefinition)
For example, Coulomb's law in Gaussian units appears simple:
where F is the repulsive force between two electrical charges, Q1 and Q2 are the two charges in question, and r is the distance separating them. If Q1 and Q2 are expressed in statC and r in cm, then F will come out expressed in dyne. By contrast, the same law in SI units is:
where $ \epsilon_0 $ is the vacuum permitivity, a quantity with dimension, namely (charge)2 (time)2 (mass)−1 (length)−3. Without $ \epsilon_0 $ , the two sides could not have consistent dimensions in SI, and in fact the quantity $ \epsilon_0 $ does not even exist in Gaussian units. This is an example of how some dimensional physical constants can be eliminated from the expressions of physical law simply by the judicious choice of units. In SI, $ \frac{1}{\epsilon_0} $, converts or scales flux density, D, to electric field, E (the latter has dimension of force per charge), while in rationalized Gaussian units, flux density is the very same as electric field in free space, not just a scaled copy. Since the unit of charge is built out of mechanical units (mass, length, time), the relation between mechanical units and electromagnetic phenomena is clearer in Gaussian units than in SI. In particular, in Gaussian units, the speed of light $c$ shows up directly in electromagnetic formulas like Maxwell's equations (see below), whereas in SI it only shows up implicitly via the relation .
Yes, I would argue that 'fundamental quantities' are indeed arbitrary, as are many of our choices, such as base-10 number systems. This is illustrated well on the Golden Record we put on voyager spacecraft, for decoding by other intelligent life; we show how fast to spin the record by relating time units in the fundamental transition of the hydrogen atom:
I'd then add that we have tried to make them as least-arbitrary (to us) as possible, but there's no reason that some other intellegence would have different 'fundamental unit' definitions and scalings, or whatever 'arbitrary' units they came up with. We could use $ (time)^{-1} $ or 'period' as our fundamental timing unit, and change all the other derived units to follow, if we wanted.
Because it was defined by measurements (the force between two wire segments) that could be easily made in the laboratory at the time. The phrase is "operational definition", and it is the cause of many (most? all?) of the seemingly weird decision about fundamental units.
It is why we define the second and the speed of light but derive the meter these days.
Best Answer
You multiply current and time to get charge. So, a coulomb is equal to one amp-second, not one amp per second, which would be division. It's the same as multiplying speed and time to get distance. Speed is km/hr, distance is (km/hr)*(hr), speed times time, which is distance.