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If an electric field in a region is found to be E = C T what is the electric potential at a radius r = 11.44 um if Co = -16.4 X 10-19 Nm4 in volts (hint: the potent...

Question

If an electric field in a region is found to be E = C T what is the electric potential at a radius r = 11.44 um if Co = -16.4 X 10-19 Nm4 in volts (hint: the potential infinitely far away is zero which is the "starting" place)?

If an electric field in a region is found to be E = C T what is the electric potential at a radius r = 11.44 um if Co = -16.4 X 10-19 Nm4 in volts (hint: the potential infinitely far away is zero which is the "starting" place)?



Answers

A solid conducting sphere has net positive charge and radius $R =$ 0.400 m. At a point 1.20 m from the center of the sphere, the electric potential due to the charge on the sphere is 24.0 V. Assume that $V = 0$ at an infinite distance from the sphere. What is the electric potential at the center of the sphere?

No, it's consider this diagram before we approach this particular problem. Three. Axis eggs. Why ends it Boeing charge. Be having Gordon. It's X Y ends it The distance between the origin and to be is you know that as small are, let's specify the unit director as I cap Z cap and Kika. These are the you the victors. So let's summation here first, and this will be our step one for this problem. So here I kept Z cap on Key Cap are the unique directors along X Y and said access respectively. Their magnitudes are considered as one does reason they're called as you directors. Okay, now, here next Imation All right, is the distance between origin and the point B. There, uh is square root off x square? Yes. Why square and serve square and is basically cold as radio distance. Let's talk about step do now Now, since it is given that we is equal to electric field and which is minus off, real times are up on Capitol are now here in this case are and real are constants having some unspecific values. So it is equal to minus self of you upon capital are and will specify the value of our here as X squared plus y square blood set square. Moving ahead will get the electric field at X is equal to minus off Doby upon do ICS, which is also known as minus of give up on de bikes off minus of you upon our multiplied by X squared les y Square. Plus it's were which is equal to we owe a phone are and we'll solve this further. That is, half times X squared plus y squared. Plus, said Square race, you have minus one and double Bye, Dad bikes off X squared plus y squared because certain square, which is equal to Rio, are going to our times two times x multiplied by X squared plus y squared Blezard square raced to minus off. Yes. Now let's do it further. Therefore, when you off, e x would be the old times X, upon capital are multiplied by X squared plus y squared. Plus that square race to mind yourself on by rearrangement that we get view times X upon our and in the square root will write it as X squared. Plus y square is a square race to minus one. We had just Serie a injuring it. So therefore it is going to be real times X. I'm going, Captain, Are my tip tired by small our race to minus one? Because we're substituting the value of our as under root off X square. Plus why square plus that square And again we are blessed ing with our similarly what we can right here even Eve I is equal to mine yourself. Do we upon the why solving further we get double minus off, double up on double Why on we can replace the value here off the as minus over you upon capital are multiplied by X square That's why square let's set square now solving for the what we get you Why easy Quit too the old times why upon capital are multiplied by our race to minus one Also, he said, is equal to minus off. Do be upon does it which is equal to be your time said upon capital R and R rest U minus one Start about district tree Now. Now we need to combine these three terms together to find the magnitude off electric field and what we get your as e bar is equal do since it's a victor. The X Times I get plus e y times Zeke up Bless easier times Do you get up that subsidy The values we you upon our time ex upon smaller I'm getting director Yes, Rio. Upon our times Why a Ponce mourner and Jacob just we you upon our said upon smaller Okay cat, let's stick to you upon our comment to the bracket. What we get X times ICAPP That's why times zika there's it times Kika do you wanted by Smaller moving it therefore e bar is equal to real upon capital are times are cap and here I capped represents the position Victor So finally, what? We can write this The potential off in electric field is Rio upon our and it's a direction is radiantly output. So this is the final answer for this particular question

All right, this is question number 22 Chapter 17. Um, the question, Basically, it's about a spherical conductor, um, off 75 centimeters radius cane, 75 centimeters. Um, the question says the electric field at the surface here, the electric field at the surface. Um, it's given us 8.4 times 10 to the four or five he played for times tend to power five volt per meter. And the question is, what is the electric potential? Uh, at this point at the surface, exactly at the surface over here. All right. Just to start with, the surgical conductor would be considered as a point charge and point chart concentrated at at the center. So what, we calculate the electric potential? A. To this point, we were gonna consider the Plain chart is 75 centimeters away from the servants, right? So this is this is the deal. Now the there there's no potential and there's no electric field. There's no, um, changing potential energy if there's no variation or Canadian in the electric field before, um, we know that the electric field as you go away from the service it's gonna change is gonna decrease right so the same thing. The electric potential is going to decrease. Asthma go away from from the surface of the office vertical conductor. So this is not our concern. The mama were concerned about the electric potential at the surface, the electric potential. The at the surface, um, is actually given by simple formula is connected to the electric field, the physical to the electric field at that point, times the distance away from a point charge or distance away from the charts. So in this case, we're gonna consider 75 centimeters. Is the distance away from the point charge, although it's a spherical conductor and we are at the surface of the conductor. But as I said, we're gonna consider this vehicle conductor as a point charge where the charge is concentrated at the center. Therefore, the distance is 75 centimeters. In this case, so v the electric potential physical to 8.4 8.4 time Stempel or five volt per meter. All right, um, times the distance this is should be measured in meters. It's 75 cent in either, um therefore, multiply by 10 to the polar or negative two meters. Alright, have to convert that. Then when you do the math, um, this is basically, uh, this is equal to 6.3 six 0.3 times 10 uh, poor five volts. All right, so before I I close this problem, I want to take it to the phe phe t simulations where we're gonna take a look at the hottest The electric potential change around, boy in charge. So we have a positive point, George here. And we have, um ah, potential indicator. The potential near, uh, the point charges Very fights, like 72 points. 17. And it decreases as we go away. Remove away from from the source. Now, the what the the electric field indicate, as indicated by the this sensor, the electric field decreases as you go away, but it decreases exponential. I mean, it decreases very fast because of the factor of form off square distance. All right, where, um, see Chris's suddenly dramatically Where the electric potential the crisis, but decreases in very slow, swift style. All right, Andi, That is how the electric provincial and electric field behave. Uh, around a plane charge. I hope this is helpful and thank you. Thank you so much.

To talk about this question. We are given the electric potential over here and we need to find the magnet during the direction of the electric field at this point. Executive to and why were 2.4. So we know that electric potential is given by negative of change and potential ratings. So that's gonna be the partial derivative with respect to X. Towards I. And the partial derivative of Y in the direction of Jacob. So let's do that. The partial derivative with respect to X. We're gonna take Y as a constant. So that's going to be a Y two x minus B Y square. That's I. Cap. And now we are going to differentiate with respect to Y. So that's a X squared minus to B X Y. So that's going to be Jacob. So this is going to be equal to X Y a minus B Y square. This is icap plus a X square minus to be expired. This is towards Jacob. So let's substitute values here, we have negative of uh two X Y. S or two X Y A uh is for minus B. Why square. This is one. And the next days we are just opening up the parentheses as well. Five X square minus to B X. Why? And this is an Jacob. Uh so let's uh let's solve this one. Um we have four times four is 16, 16 times 160.46 point four. So we have 6.4 minus .4 square times it is going to be 1.2 I minus. This will be 20 Minour that will be four times eight times 0.4. So that's going to be 12.8 cheap. So if you can provide us further, This becomes a uh -7.2. J This part and This part becomes 6.4 -1 point away. So that's gonna be negative five point 12, I think it a 5.12. Hi cap. So this is the required electric field. Uh now this is in the vector form, but we need the magnitude and the direction. So the magnitude is going to be a square root of 5.12 square plus 7.2 Square. So that's going to be equal to the square plus 7.2 Square and square out of this, there's going to be eight 83. Uh Newton for cooler. So that is the magnitude of the electric field and we need to find that direction as well. Uh so clearly this is both the corners and negative. It means that it is pointing somewhere over here. So we can find a direction by finding this angle alpha and then uh adding uh perhaps 1 80 degrees to it. So we can get the angle with respect to the positive x axis. So, the anger tunnel for it's going to be uh the y coordinate or the X coordinate. So that's gonna be negative 7.2 over negative 5.12. So a figure of a calculator, that's going to be 7.2 divided by twice 0.1 to 10. And worse of this comes at 54.58 degrees. So the total angle it's called tita is going to be 1 80 degrees plus alpha and uh valuable phobia. Well, we already have, so that's gonna be 2 34 .58°. Uh We're gonna say this is counter clockwise with respect to positive X. Axis. This is the direction. Thank you.

Conducting solid sphere of radius capital R equals to 18.0 centimeter. And the Charles Q. Which is 6.10 into 10. To the power minus six color. Okay, so we have to calculate the electric potential at 60.24 point zero centimeter from the center that is point A. And to the point B. And to the point C, which is center. So first of all drawing the diagram for this question. So I suppose this is our spear and these are the points. Okay, so this is the line. Okay, so this is the center of the spear and this is the point on the surface and this is the point A. Which is located at a distance this 24 centimeters so R is equal to this value. Okay, so we can see that this is Pierre is conducting. So it means the potential at point C. And B will be equal. So we can first calculate we B equals two. We see this will be equals to take you by capital. Are so substituting values here. So we get K which is 8.9875 Multiplied by 10 to the power nine newton meters square. Particular atmosphere molecular by Q. Which is 6.10 into 10. To the power minus six column. They were by radius R. Which is 18 centimeters 18.0 to 10 to the power minus two. So from here we be or NBC comes out to be 3.5 multiplied by 10 to the power five world. Okay, so these are the answers for DVD and VCD. Okay, now we can calculate the potential at point A. So this will be equals two Kq by small. Are here will be small. Are so potential at a This will be equals two Kq by small. Are so now we can substitute values so we get 8.9875 multiplied by 10 to the power nine manipulated by Q, which is 6.10 and 2 10 to the power minus six column develop a distance R, which is 24 centimeter, so 24 manipulated by 10 to the power minus two m. So from here, solving we get potential at 0.8 equals to 2.28 manipulated by 10 to the power five vote. Okay, So this becomes the answer for the potential at point. Okay?


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