Small doubt regarding electric charge

[cptolemy]

Good morning

I'm no expert in classical physics, so I have one doubt. If I have a body with mass M, and I charge it electrically with x C (Coulombs), will its mass remain the same, or will it change (in which amount)? Can you help me in the case of a ball, let's say, with 1.5 Kg charged with 0.5 Coulombs?

Also, in the case of an electron usually charged with 1.6E10-19 Coulombs, will its mass be bigger or smaller than if it was in rest (I believe to be 9.1E10-31 kg), and in what amount?

Or will the mass change - in either case - only if there's an interaction with another body (repulse or atraction)? Forgive my ignorance.

Clear skies,

 

[mjc123]

I don't know what you mean by "an electron usually charged with 1.6e-19 C". The electron has an intrinsic charge of -1.6e-19 C, you can't add it or take it away, and you can't change the mass in that way.

In the case of the ball, suppose the charge is added by adding or removing electrons. How many electrons correspond to a charge of 0.5 C? What is the mas of these electrons? How does it compare with 1.5 kg?

 

[cptolemy]

Hi

Ok, then the ball seems simple enough to solve. I divide 0.5 by the module of the electron's charge, and multiply by the electron mass and sum it up to 1.5 - is this correct? But I get a value of 2.84375e29 + 1.5 Kg?...

Regarding the electron, I was thinking on that: the mass of the electron is the same without its charge hipotetically?

I am really a newbie on this (sort of) - thus I'm asking some help

Clear skies

 

[jbriggs444]

Ok, then the ball seems simple enough to solve. I divide 0.5 by the module of the electron's charge, and multiply by the electron mass and sum it up to 1.5 - is this correct? But I get a value of 2.84375e29 + 1.5 Kg?...

The approach seems sound. You divide total charge by charge per electron to get the number of electrons. And you multiply by the mass of a single electron to get the total mass. But please show your work. Which constants did you find for those two quantities?

 

[cptolemy]

Hi

So the charge is 0.5 C. If I divide this by 1.6E10-19 C I get 3.125e18 electrons. Multiplying this by the mass of one electron 9.1E10-31 kg, I get 2.84375e29 Kg. And I must add 1.5 Kg from the ball...

Is this really right?...

 

[Vanadium 50]

Is this really right?...

No. Check your math.

 

[cptolemy]

Oh...I placed a 2 instead of 1 in the exponent (I did not copy pasted from a calculator). So it's 2.84375e19 Kg?

 

[jbriggs444]

Oh...I placed a 2 instead of 1 in the exponent (I did not copy pasted from a calculator). So it's 2.84375e19 Kg?

No. That's still off by about thirty orders of magnitude (thirty-one to be exact).

When unsure about a mathematical result, a sanity check is a good thing. What is -31 + 18? Is it positive or negative?

At a guess...

You are using a Windows calculator. You keyed in "3 . 1 2 5 E 1 8 * 9 . 1 E - 3 1 =" and read off the result.

What you did not realize is that that the calculator parses this as $(3.125 \times 10^{18}\ \times\ 9.1)\ -\ 31$

What you wanted to have keyed in was "3 . 1 2 5 E 1 8 * 9 . 1 E 3 1 ± =". The plus/minus key inverts the exponent for data entry to Windows calculator. [Not what I would have expected until I tried it].

To repeat the lesson -- if a calculator tells you one thing and a sanity check tells you another, do not trust the calculator.

 

[cptolemy]

Ok - this is a mistery. If I make the math by hand, I get 2.84375e-12 Kg.

BUT. if I make using the calculator SpeedCrunch, I get:
0.5/(1.6e-19)*(9.1e-31)
= 2.843750000000000e19...?

Of course the hand made is right (the first). I don't understand this error in SpeedCrunch. It NEVER happened. :/

 

[mjc123]

Regarding the electron, I was thinking on that: the mass of the electron is the same without its charge hipotetically?

There is no such thing, even hypothetically, as an electron without its charge. But its antiparticle, the positron, has a charge of +1.6e-19 C, and the same mass as the electron.

 

[jbriggs444]

I don't understand this error in SpeedCrunch. It NEVER happened. :/

See the guesswork editted into #8 above.

 

[cptolemy]

Ok. Using () in all the input I get:

(0.5/(1.6e-19))*(9.1e-31)
= 2.843750000000000e-12

Usually I don't have to do this. Also, in decimal model (not scientific/engineer) I don't get this error - I get the correct value. I'll download the latest version.

As for the positron, I knew that, but it's actually fascinating. My real doubt was to know if the charge could contribute somehow in the mass of the particle. A little bit like the quarks which compose the protons for instance: the sum of their masses, per se, it's a small percentage of the total mass. The interaction must be taken into account, I believe.

 

[vanhees71]

Ok - this is a mistery. If I make the math by hand, I get 2.84375e-12 Kg.

BUT. if I make using the calculator SpeedCrunch, I get:
0.5/(1.6e-19)*(9.1e-31)
= 2.843750000000000e19...?

Of course the hand made is right (the first). I don't understand this error in SpeedCrunch. It NEVER happened. :/

Strange! My speed crunch gets the right result without quibbles. I'm working with linux though...

 

[ZapperZ]

Ok. Using () in all the input I get:

(0.5/(1.6e-19))*(9.1e-31)
= 2.843750000000000e-12

Usually I don't have to do this. Also, in decimal model (not scientific/engineer) I don't get this error - I get the correct value. I'll download the latest version.

As for the positron, I knew that, but it's actually fascinating. My real doubt was to know if the charge could contribute somehow in the mass of the particle. A little bit like the quarks which compose the protons for instance: the sum of their masses, per se, it's a small percentage of the total mass. The interaction must be taken into account, I believe.

This thread has become a very confusing jumble of mass=charge and calculator error.

Here's the deal: charge has no mass. Charge CARRIERS may have mass.

If you have a ball that has no charge, and then you charge it (either by removing electrons or adding electrons), then yes, in principle, you have changed its mass because you have removed or added particles to it. HOWEVER, this is extremely minute when compared to your 1.5 kg mass! Try it! See how much mass has changed to charge a 1.5 kg mass by, say, 10 nC (which is a huge charge). You will need a bit more decimal places to see the change.

And no, you cannot separate out electrons from its charge. An electron with no charge is not an electron, since an electron is DEFINED as having that charge, and all the other properties associated with it.

Zz.

 

[vanhees71]

Well, and to be very pedantic you haven't only added the mass of the charge carriers but also the mass due to the energy of the electrstatic field (in the restfame of the body)...