# I Electric Field Strength-conceptual question

Tags:
1. Dec 15, 2016

### iochoa2016

Electric Field Strength is defined in many books as F/Q, where F is force and Q is the test charge. but why is that? why not F/(2Q)? or F/Q^2?, is this word "strength" related to stress-strength as in mechanics?

2. Dec 15, 2016

### Delta²

Electric field strength is simply the strength the electric field applies per unit of charge. It is the same to say F/Q or F'/2Q or F''/Q^2 (where F' is the strength the field applies to the 2Q charge, F'' the strength it applies to a Q^2 charge).

3. Dec 15, 2016

### Staff: Mentor

That's actually two questions, with two different answers. The $F/2Q$ thing is just a matter of the units that we choose: We could decide to measure the force $F$ not in Newtons but in some new unit that I will call the "greeple", defined by saying that there are two newtons in a greeple the same way that there are six feet in a fathom.... And suddenly that factor of two would appear in the law, and it would disappear as quickly if we went back to Newtons.

The $F/Q^2$ thing is completely different. We observe that at any given point, there is a force of $F_0$ on a particle of charge $Q_0$, but that there is a force of $2F_0$ on a particle of charge $2Q_0$ and a force of $3F_0$ on a particle of charge $3Q_0$. No amount of playing with the units or other constants can reconcile these observations with a $F/Q^2$ rule.

4. Dec 15, 2016

### iochoa2016

Hi, Thanks for the answers. Still is not clear for me the word "strength". Strength (as i understand) is the capacity of a mater to handle a certain stress. as E is a medium (field or substance) then its strength is defined as F/Q, so when a test charge Q is placed in the field, a force appear on the test charge, this will stress the field E with a force based on Coulomb Law F', so based on stress-strength concept this forces no need to be equal however in electromagnetic they are, so F'=F? why??? is this reasoning correct?
Also, it is said that E definition is an analogy to gravitational filed where g=F/m. But i cannot find a link between the two concepts. g means acceleration and is the second derivative of distance. so then E=F/q, E is acceleration too???

5. Dec 15, 2016

### Ibix

"Strength" is also the ability to apply force. Am I strong enough to lift this weight? That's the sense it's being used in here.

With regard to your last question, the analogy with gravity is that mass is the "gravitational charge" - the source term for the gravitational field. This is analogous to electric charge being the source term for the electric field. A sensible measure of field strength is how hard it shoves a unit of whatever it affects (mass, or charge), which is why field strength is F divided by whatever.

Gravity has the odd property that how hard it shoves (mass is the gravitational charge in $F=GMm/r^2$) is the same as how hard it is to shove something (mass is the resistance to change in motion in $F=ma$). So gravitational field strength is just acceleration, but other fields' strengths will not be.