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ConstantsIn this example will use the quantization of charge to delermine Ihe number excess electrons in an object: (a) A large lastic block has charge of 1.0 pC .0...

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ConstantsIn this example will use the quantization of charge to delermine Ihe number excess electrons in an object: (a) A large lastic block has charge of 1.0 pC .0 X10 How Asay moro electrons than protons aro in tho block? (b) When rubbed with silk cloth; glass acquires_ nel posilive charge ol 1.0 nC . Il the rod contains 0 mole of molecules; what fraction of the moleculos have been stripped of an electron? Assume that at most one electron emoved from any molecule:SOLUTIONSET UP AND SOLVE Part

Constants In this example will use the quantization of charge to delermine Ihe number excess electrons in an object: (a) A large lastic block has charge of 1.0 pC .0 X10 How Asay moro electrons than protons aro in tho block? (b) When rubbed with silk cloth; glass acquires_ nel posilive charge ol 1.0 nC . Il the rod contains 0 mole of molecules; what fraction of the moleculos have been stripped of an electron? Assume that at most one electron emoved from any molecule: SOLUTION SET UP AND SOLVE Part (a): We want t0 find tne number of electrons N needed for net charge object: Each electron has charge We divide Ihe tolal charge by ~LUxlO 6.2 x 1012 clcctrons CluUX 1.0 x 10-6 C on Part (b): First we (ind the number Nion of positive ions needed Iotal charge of 1.0 nC each ion has charge +e_ The number of molecules in mole Avogadro's number; 6.02 102 50 the rod contains 6.02 1033 molecules_ part (a) , we divide the total charge 5 on the rod by the charge of one ion: Remember that #C C. Thus, Nion L0XIQ 1.6*10 6.25 109 The fraction all thc molecules that arc ionized 6.25x 10" 6.02*102 1.0 * 10-14 6.02x108 REFLECT charge imbalance about 10-1 is typical for charged objects. Common objects contain huge amount of charge, but they have very neary aqual amounts positive and negative charges. Part A - Practice Problem: A tiny object contains 25*1012 protons and 80x1012 electrons; What is the net charge on the object? Express the net charge In Coulombs two slgnificant flgures. AZd 232 Submit Previous Answers Request Answer Incorrect; Try Again; attempts remaining



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CALC The one-dimensional calculation of Example 42.4 (Section 42.3$)$ can be extended to three dimensions. For the three-dimensional fce NaCl lattice, the result for the potential energy of a pair of $\mathrm{Na}^{+}$ and $C^{-}$ ions due to the electrostatic interaction with all of the ions in the crystal is $U=-\alpha e^{2} / 4 \pi \epsilon_{0} r,$ where $\alpha=1.75$ is the Madelung constant. Another contribution to the potential energy is a repulsive interaction at small ionic separation $r$ due to overlap of the electron clouds. This contribution can be represented by $A / r^{8},$ where $A$ is a positive constant, so the expression for the total potential energy is
$$U_{\mathrm{tot}}=-\frac{\alpha e^{2}}{4 \pi \epsilon_{0} r}+\frac{A}{r^{8}}$$ (a) Let $r_{0}$ be the value of the ionic separation $r$ for which $U_{\text { ot }}$ is a minimum. Use this definition to find an equation that relates $r_{0}$ and $A,$ and use this to write $U_{\text { ot }}$ in terms of $r_{0 .}$ For $\mathrm{NaCl}$ , $r_{0}=0.281 \mathrm{nm} .$ Obtain a numerical value (in electron volts) of $U_{\mathrm{tot}}$ for NaCl. (b) The quantity $-U_{\text { tot }}$ is the energy required to remove a $\mathrm{Na}^{+}$ ion and a $\mathrm{Cl}^{-}$ ion from the crystal. Forming a pair of neutral atoms from this pair of ions involves the release of 5.14 eV (the ionization energy of $\mathrm{Na}$ ) and the expenditure of 3.61 $\mathrm{eV}$ (the electron affinity of Cl). Use the result of part (a) to calculate the energy required to remove a pair of neutral Na and Cl atoms from the crystal. The experimental value for this quantity is $6.39 \mathrm{eV} ;$ how well does your calculation agree?

Okay, So early, American to off the force. Can we go to mass times acceleration, which also can you go to the ah abs value Charge Cube. Testy. That review. So if it doesn't rain from here we have the man is you off the charge Cube over. M is you will overeat. So for party, we know that the potential difference between point B and C can we go to graduate few tents. The landfill rock which will have easy with BBC over our So now have few over. M is you go to a over BBC about which is he was a are over BBC. So for Parsi. Well, we know that the left end of the rock is negatively charged. And the Ryan of the Rock is positively charged. And we know that, um, the Ryan of Iran should have the higher potential, which means that policy has higher potential. Seems easy. Eddie Ryan. All the rot. So for party. While we know absolutely few over em is equal to a over B b. C. So we have a is able to absolutely a few tens BBC over. And now So now the charges given as an active 1.6 times 10 to the part of the neck. 19 Cool on in a mass of the utterance isn't 9.11 times 10 to the power of a negative 31 kilograms. The potential difference is given as one million votes, which is one times 10 to the power of 93 boats and a length of rice. Cubans 2.5 meter. So now it's quite invested equation to determine the explorations, which is, you go to absolutely inactive 1.6 times, 10 to the power off next of 19 cooler multiplied by, uh, maybe see, which is, uh, one times tend to the car off her negatory waltz over ML, which is 9.11 times 10 to the power off. Negative, 31 kilograms, 10 times 0.50 meter. And we know this is equal to 3.5 times 10 to the power of eight. Meet over second square. So now let's take a look at party. While the reason why, um, the actual experiment used a rotating school within wire is because rotating school everything work can make a peritus a move very large distance and high speed. Also, we can calculate the total potential by counting, uh, the potential in each turn since rotating spool of wire can have many turns, a wire and these are the answers for this question.

We are given you. It was negative. Alfa Israel over fall by absolutely not are thus over our dressed the part of eight. So do you. D r equals zero. We have to do this to minimize you. So we have, uh are not to the seventh. It was eight. A times four by as the not over Alfa is square And using this, we find the minimum value off you is given by as far a swell over four by not times. Not anyone over our thus are not to the seventh over eight. Part of the eight. Sure it was negative. Seven as far is where over 32 by s are not are not. I'm putting in the values we have. You mean it was negative? Negative 1.26 times 10 to the negative 18 jewels which is negative 7.85 Is that transport

Hi in this given problem there are the two charged particles of course Cuban. The first charge particle that is put that and another charged particle. You too that is put at a point B midpoint between them is P whose distance from both the charged particles. It's given us 5.0 centimetre. Now in the first part of the problem, most of all the magnitudes along with the sign over these charges are human Is equal to plus 20 Into 10 for -8 column and you do is minus by 0.0 Into 10 for -8 cola. So in this first part of the problem we have to find net electric field at this midpoint B you know Electric field always goes away from the positive charge and approaches a -1. So at point B electrical due to a that will be going away and electrical you to be that will be approaching it. In this way we conclude both of these electric fields will be added to give the net electric field means here it will be E A less E B. No for E A. This is scared into Cuban by our square or E B. Again, this is scary into Q two Y. The stands will be seen as our whose value here is given as 5cm now logging in all the non values here. Okay, this is nine into 10.9 Newton meters square park Boulami squad understands that is one by five into 10 days par minus to meet her the whole square and we are taking them as a common out leaving behind Cuban which is 20 In to tenders par -8 column and let's kill two. We will use its magnitude only not the direction because direction because negative sign has already been used in direction. That will be plus five into Bandage bottom -8 Fulham. So finally this electric field here will be given by nine In 2 10 days to the part nine In 225 into 10 dish part -8, divided by 25 again Into 10 AR -4. So finally here this electric field comes out to be nine into And it's the bar five new turn park along which is the answer for the first part of this problem. Now, in the second part of the problem we are pudding charge U. Is equal to minus or find zero Into a 10 for -8. Fulham. Yeah. Wine feet. So this charge will experience a force F equals two Q into E. And as this is a negative charge. So it will experience a force towards positive charge means towards left in our direction opposite to that electric field which we have found at point P which was towards right. So this force here will be given by 4.0 into Bandage for -8 Ghulam multiplied by electric field which is nine in 2 10 days apart pipe Newton park colon answer which is the answer for the first part of this problem. So finally, force here will be given by have is equal to 0.036. Newton answer for the second part of this problem and that will be acting the words left. No. Finally in the 3rd part of the problem we have to find a point at which electric will will be zero. So as the two charges are unlike, so electric field between them being same being in the same direction at all, the points Will be known zero everywhere And it is zero At any point on the line joining the two charges and beyond that charge which is having smaller magnitude. And here in this problem that is smaller magnitude. Charge Is -5.0 into 10 days par -8 columns are supposed observation point is this that would be all at a distance of X wrong going to be so at this point there will be two electric fields and both of them should have same magnitude but opposite direction things we can say electrical at all due to a would be elected, it should be equal to electrical that boat you to be now using the expression for elective field for E at all due to end this is scared Into charge which is 28-10 for -8 divided by distance and it comes out with 10 plus x centimeter square because to get into Why into bandage for -8 divided by the stands. That is X is quite only cancelling this K Cancellelling an eight for -8 and five borsa 20. No writing it as a whole square, it becomes to buy 10 plus X. The whole square is equal to one by X. The whole square ignoring the negative sign. And now taking the square root, this is to buy 10 plus X is equal to one by X. So making a cross multiplication. Finally we get the value of X To be equal to 10 centimetre, the words right of you do, Which is the answer for the 3rd and the last part of this problem. Thank you.


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