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What is the capacitance of a drop that results when two mercury spheres, each of radius $R=2.00 mathrm{~mm}$, merge?...

Question

What is the capacitance of a drop that results when two mercury spheres, each of radius $R=2.00 mathrm{~mm}$, merge?

What is the capacitance of a drop that results when two mercury spheres, each of radius $R=2.00 mathrm{~mm}$, merge?



Answers

A spherical capacitor is formed from two concentric, spherical, conducting shells separated by vacuum. The inner sphere has radius 15.0 cm and the capacitance is 116 pF. (a) What is the radius of the outer sphere? (b) If the potential difference between the two spheres is 220 V, what is the magnitude of charge
on each sphere?

So they want the capacitance. We have a radius of five centimeters or we can say point zero five meters. We have a separation d of two point eight millimeters or we can say point zero zero two eight meters. We have the dialectic constant of Mika equaling seven and then the primitive ity of the electric primitive ity of free space equals eight point eight five times ten to the negative twelve a school I'm squared per Newton meters square. So at this point we can say that C is going to be equal to a dialect constant times the electric primitive ity of free space times the area divided by dear. We know that the area for this is going to be equal to pi. R squared soc is going to equal pi r squared k absolutely not divided by D and we can solve and say that c is going to be equal to pi. Point zero five squared the dialectic constant of seven times eight point eight five times ten till native twelve all divided by D the separation of point zero zero two eight and we find that the capacitance here is going to be one point seven three times ten to the negative tenth fares. So this would be our answer. That is the final end of the end of the solution. Thank you for watching.

No. Here we are discussing the problem based on competence. As you know, that distance can be the finance charge Would, by the end of what you need to put a gender difference, induct problem it just give it There is a spectacle. Conductor off radius R So this is the spherical conductor Off radios are on on which Q charge is given. So if you charge is given to this conductor, then put angel on its surface. So here, if que judge is given Buddha is very good conductor. No, all the radius r then what a nation ordered surface que upon full by? Actually not No, this conductor, it's surrounded by and their conductor off in finance radius this conductor fish Sit down big bite and they're conducted. Oh, and by night radius So potential on the surface is zero Put a shirt on its surface It will be zero and potentially friends between the surfaces would be no substitute the video So God stints, baby you upon the baby No potential difference here You, upon food bite have not are on simplify You will get cap pistons to be food by Absolutely not are so we can see the cap. Astin's office Medical conductor? Yeah, pistons off spectacle. Conductor is directly proportional to radius more. Is the radius more ability that Pakistan? So this is very important point to be noted, dog for hysterical conductor Constance is darling Live was not do its various not second part being the people are we have major that happenstance of start If what it considered to me will be a hysterical body off radius six Sergeant three and get 80 kilometer. But what this Bedouin meet it so 6380 in tow 10 to the power three meter, then ex cap assistants. Then Captain stands off the others full by afternoon not are We will substitute the value in it for by his 3.1 full afternoon. Not is primitive ity off free spits on its numerical value is it went five for can do the part of mine esperan on radius 6380 pen Moody poverty Ferron, If you solve it, we will get 0.710 And don't tend to depart minus four better or a weekend writing 71 Jiro Micro favorites of the sedans are of this problem

Now in this problem, it is given there are boots and put in place often idiots. 5 10 Give it We're converting this man into a meeting. These two places are subjected about by the restraints off three quite door millimeters that it you do and tend to be powered by the three meters. If there is your my courtesy Between the learning there is a Michael between the place on if the dialectic constant is you 0.6 So exc abstinence be a local play Captain and Captain Strains will be. He ain't going afternoon, not a 20. We are substituting governor evenly by here is by your squid. Yeah, obviously. So we can write he find one foot who is where divided by distance and dispenses given so on. Suddenly we will get cap space will be what quite doodle age six And to tend to the public minus pain Better. So this is about

All right. It's a human problem. We are having, uh, spherical capacitor in rich Did our your on San Prigge spheres metallic spheres Holloman can experience but you know, is having a radius A and outer is having a radius be. And this radius a is given asked 15 point Tzeitel, senti Niedere All we can say this is little 0.1 cry meter the inner sphere. The radius off this outburst here? Yes, Missing It is known. It is not given to us. You have to find it. Then the capacitance off Such a capacity is given as 100 and 16 bqool. Patty, this is the capacitance off the hysterical capacity. No. In the first part of the problem, we have to find the value off this outer radius. For rich muse, the expression for capacitance off our surgical capacity. Riches port by absolutely not into a into B divided by B minus it. So if we put all the given values, this is 116 into 10. Dish for minus well is equal to one by nine into tenders for nine. For the value of this four by epsilon. No in do okay, which is 0.15 but interviewed Yes, in Toby, which is missing the apparatus. And here it becomes the minus zero Boring one fight. So making a cross multiplication. Here we get 116 multi card, but finished one minus well into nine into condition for nine. Reckitt, be fine. US Macedo 0.1 pipe is equal to 0.1 by in Toby. Then the expand the bracket in the Quran site you get Yes, he is 1.0 or for eight times will be minus 0.1566 is 4 to 0.15 times will be. Then you sure? 0.15 b from right inside to the left hand side and it will be subtracted from 1.44 b, giving us simply zero point it 94 time. So be and, uh right inside would become 0.1566 So finally the value of this be I'm self will be 0.1566 divided by 0.894 What you can see final answer for this outrageous is you don't want one 75 meter. This is the answer for the plus park? No. In the second part off the problem this first park. And also we didn't US 17.5 sent UNITA? No, For the second part of the problem, we have to. We have been given the potential applied across these two stairs, which is true 20 world Naevia to find the charge over both of these stairs. But the charges going as c like a bread gravy. So here it becomes 116 into 10 to the power minus trail padded. I lied by through 20 more. So this pretension finally comes out to be you'll 0.5 by It's a rendition part, minus it more. This is the answer for the second part off. Thank you.


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