Interpreting Tipler & Mosca: Electric Field

[NeuronalMan]

Hello, maybe this is the wrong place to post this, but I'll give it a try. It's not a homework problem, but rather how to interpret my textbook.

I'm using Tipler & Mosca and I find the section about the electric field kind of slippery. It defines the electric field as in many other sources, e.g. wikipedia; if you put a small positive test charge q at some point near e.g. three point charges, there will be a net force exerted on q by the three other charges.

That's okay. The part I don't understand is where it says that "because each of these forces is proportional to q, the net force will be proportional to q." Can that be shown using Coulomb's Law? So, the greater the charge is, the greater the attraction between the charges will be?

Then it says that, in addition, q will exert a force on each of the other point charges. And because these forces on the other charges might cause some of the other charges to move, the charge q must be so small that the forces it exerts on the other charges are negligible.

But if anything, the forces from q on the other charges will be equal to the forces from the other charges on q? If not, that keeps the whole idea from being what we talked about.

To me, the way in which this is shown just doesn't make any sense.

 

[tiny-tim]

Hello NeuronalMan!

… The part I don't understand is where it says that "because each of these forces is proportional to q, the net force will be proportional to q." Can that be shown using Coulomb's Law?

Coulomb's Law has the force proportional to qQ/r², and in particular is porportional to q.

It's (exactly) like the gravitational force on a mass m being proportional to m.

Then it says that, in addition, q will exert a force on each of the other point charges. And because these forces on the other charges might cause some of the other charges to move, the charge q must be so small that the forces it exerts on the other charges are negligible.

But if anything, the forces from q on the other charges will be equal to the forces from the other charges on q? If not, that keeps the whole idea from being what we talked about.

It matters if the charge which is being measured moves, beacuse that changes the measurement.

It doesn't matter if the test charge (q) moves, because it has to move …

that's how the measurement is made!

It's like measuring the force of gravity on the Moon with a test mass …

if your test mass is an asteroid almost as large as the Moon, then that won't give you the right result, will it?

 

[tiny-tim]

Thanks for your reply,
I guess it's kind of sorted, but there's still something I don't get.
Are you saying that the net force exerted by q on q1,q2,q3 is not equal in magnitude to the net force exerted by q1,q2,q3 on q?
In my book, it looks like the arrows are the same length.
And E being F/q, increasing q1,q2,q3 would presumably make E greater, according to Coulomb's Law. But then, the force exerted by q on q1,q2,q3 should be equal in magnitude.
I'll try to see how this is done in Sears and Zemansky.

No, the forces are the same

if q is very small, the effect on q₁ q₂ and q₃ will be very small, so we're not disturbing them

the force on q will be the same, also very small, but that's fine … we're perfectly happy measuring a very small effect