Let's say I have only one nut and after rubbing the straw, the nut is attracted to it, so if I put the straw far enough so that the nut can't touch it, what would be their distance ##r##, when I then want to use formula ##F_\mathrm e=k\frac{Q^2}{r^2}##? The distance between the center of mass of the charged part of the straw and the center of mass of the nut? And will their charges have the same value? I think yes, but I am no sure. I think I know how to conduct the measurement now, but I need to make sure I understand some crucial points.nasu said:You transfer charge from straw to both nuts at the same time or one after the other? But either way, I don't see why would you expect the nuts to end with the same charge.
Why do you need to be able to say that?Lotto said:So, I have tried to rub two tied balloons against my hair and they were repeling each other, but the problem is that I need them to have the same charges, so that I can say ##F_\mathrm e=k\frac{Q^2}{r^2}##.
Since I must determine ##Q## of the straw. I must use this equation ##Q(t)=Q_0 \mathrm{e} ^{-\frac{\sigma}{\epsilon}t}##. So when I calculate ##Q## (by using geometry) and know its ##t##, I can use fitting with an amount of these datas and determine ##\sigma##.haruspex said:Why do you need to be able to say that?
If the initial charges are q0 and Q0, what is the repulsive force at distance r, time t?
Do you? Please answer my question in post #33.Lotto said:Since I must determine ##Q## of the straw.
The repulsive force is ##F_\mathrm e =k\frac {q_0 Q_0}{r^2}## in this case, but I must be able to calculate ##Q## of the straw dependent on time, see post #12. I can do so by measuring the distance ##r##, and then by using geometry, I can determine ##F_\mathrm e## thanks to the deflected nut/washer. Then I calculate ##Q## as ##Q=2r\sqrt{\pi \epsilon F_\mathrm e}##.haruspex said:Why do you need to be able to say that?
If the initial charges are q0 and Q0, what is the repulsive force at distance r, time t?
You did not answer the question I asked. What is the force at time t? What is the ratio between that and the force at time 0?Lotto said:The repulsive force is ##F_\mathrm e =k\frac {q_0 Q_0}{r^2}## in this case, but I must be able to calculate ##Q## of the straw dependent on time, see post #12. I can do so by measuring the distance ##r##, and then by using geometry, I can determine ##F_\mathrm e## thanks to the deflected nut/washer. Then I calculate ##Q## as ##Q=2r\sqrt{\pi \epsilon F_\mathrm e}##.
I am not sure whether I understand, but $$F_\mathrm e (t)=\frac{Q_0 k q}{r^2} {\mathrm e}^{-\frac{\sigma}{\epsilon} t}=F_\mathrm{e_0} \left(\frac{r_0 }{r }\right )^2 \frac{q}{q_0} {\mathrm e}^{-\frac{\sigma}{\epsilon} t}.$$ Soharuspex said:You did not answer the question I asked. What is the force at time t? What is the ratio between that and the force at time 0?
Well, I am actually supposed to determine ##Q## dependent on time, see post #12.nasu said:You don't need the actual values of Q and Qo. And it would be very difficult to find them. You just need to find how the ratio ##Q/Q_o## depend on some distance or angle in your specific setup. Then you will plot this (distance or angle) versus time.
No, it says find the product of the charges, qQ. But if the purpose is to find ##\sigma## then you do not even need to find that.Lotto said:Well, I am actually supposed to determine ##Q## dependent on time, see post #12.
There is no such requirement in the post #12. Using that formula does not mean that you need to know Q.Lotto said:Well, I am actually supposed to determine ##Q## dependent on time, see post #12.
Since you are working with two balloons, both discharging, the equations are $$F_\mathrm e (t)=k\frac{Q(t)q(t)}{r^2} =k\frac{Q_0q_0}{r^2} {\mathrm e}^{-2\frac{\sigma}{\epsilon} t} =Lotto said:I am not sure whether I understand, but $$F_\mathrm e (t)=\frac{Q_0 k q}{r^2} {\mathrm e}^{-\frac{\sigma}{\epsilon} t}=F_\mathrm{e_0} \left(\frac{r_0 }{r }\right )^2 \frac{q}{q_0} {\mathrm e}^{-\frac{\sigma}{\epsilon} t}.$$ So
$$ \frac{F_\mathrm e (t)}{F_\mathrm {e_0}}=\left(\frac{r_0 }{r }\right )^2 \frac{q}{q_0} {\mathrm e}^{-\frac{\sigma}{\epsilon} t}$$
But why do we need it?
I understand, but I won't do it with balloons, I will do it this way: I will rub the straw and then made the washer deflect because it will be attracted to the straw (but the straw will be far enough so that it won't touch it). Then I will measure the distance between the washer and the straw. What can I say about their charges? If the straw has a charge ##Q##, what charge has the washer? It is attracted, so it must have a charge, maybe only a partial one, but still some. Isn't its charge the same as ##Q## (in value)? Or are their charges different? I know it doesn't matter, but it interests me.haruspex said:Since you are working with two balloons, both discharging, the equations are $$F_\mathrm e (t)=k\frac{Q(t)q(t)}{r^2} =k\frac{Q_0q_0}{r^2} {\mathrm e}^{-2\frac{\sigma}{\epsilon} t} =
F_\mathrm{e_0} \left(\frac{r_0 }{r }\right )^2 {\mathrm e}^{-2\frac{\sigma}{\epsilon} t}$$.
Using the angle, you will measure F(t) and r(t), so you can plot.. what against what to find ##\sigma##?
Since the problem statement only expects you to be able to find the product of the charges, the question setter clearly understood that you cannot find the individual charges in the asymmetric (washer and straw) model.Lotto said:Or are their charges different? I know it doesn't matter, but it interests me.
And I still think that when I am to measure the dependence of the straw's self-discharge on time, I am to measure its ##Q## dependent on time, but that is only my opinion.
No, even an uncharged conductor will be attracted because of the induced charge distribution.Lotto said:what charge has the washer? It is attracted, so it must have a charge,
And can I say that the washer has a partial charge, that it has on one side a negative charge and on the other side a positive charge?haruspex said:No, even an uncharged conductor will be attracted because of the induced charge distribution.
If this is in the case where you touched the straw against the washer, both will have a negative charge overall, and the side of the washer away from the straw will be negative.Lotto said:And can I say that the washer has a partial charge, that it has on one side a negative charge and on the other side a positive charge?