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(a) What is the direction and magnitude of an electric field that supports the weight of a free electron near the surface of Earth? (b) Discuss what the small value for this field implies regarding the relative strength of the gravitational and electrostatic forces.

a)5.58. $10^{-11} \frac{\mathrm{N}}{\mathrm{C}}$b)Gravitational force is extremely small compared to the electrostatic force.

Physics 102 Electricity and Magnetism

Chapter 18

Electric Charge and Electric Field

University of Michigan - Ann Arbor

Hope College

University of Sheffield

McMaster University

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to solve this question, we must know, was the weight off electron. So wait off electron, which is gravitational force of attraction. So let's write it as f g. So it means weight off electron. Um, that is massive electron times gravity on DDE. We are asked about the electric field which will support the gravitational force. Oh, the weight off electron. So force electric force is equal to charge which is electronic charge in this case, times E. So since election has negative charge, we have a negative sign there. Now we want to make a equality between gravitational force and electric force. From this, one can find electric field by just taking if j divided by electrons charge. So let's take the magnitude for now. In this case, E is equal to myself. Electron times gravity divided by Elektronik Charge Massive Phillip tries 9.11 So let me correct it. 9.11 time stand power negative 31 kilograms. Remember that your mask should always be in kilograms times gravity which is 9.81 divided by charge. An electron is 1.6 times 10 power negative, 19 cooler. So if you perform this calculation, you will get 5.58 times 10 power, negative 11. So if you don't want to calculate so much, you can just see that this is nine. This is approximately 10 so nine times Chinese, it's 90 divided by 61.6. So 90 rewarded by 11.6 has Valley, which is close to six because 16 times six is 96. So our numerator is close to 90 so it must be less than six. So it's 5.58 I'm 10 power negative. 11 comes from factor of 10 power negative. 31 in 10 power. Negative 19 here. So these division views you're just 10 power negative. 12 on the division off 9.11 times 9.8 divided by 1.6 year gives you 55.8, so actual answer will be 55.8 times 10 power. Negative. 12. So that is this. So units here should be Newton per column. So this is the electric field one needs to have on Let's discuss the sign of electricity so you can see that there is a negative sign here. So but the fourth year is a tractor, so we want. So let's say this is so awful And this is electron here, gravitational forces pulling downwards. You want the force off electricity, too? Apply a poor force. No. You know that if electric field points upward, electron will be attracted to the service off both. That's a E. And this should be fools here because electric field here and force here have opposite relation. That force is negative off electric field. So what we must have instead of this electric field 20 in downwards. In that case, you will have electric feel electric force pointing upward as here as it shows here, and so that electron will will levitate. Now let's solve for the party hard be asks about comparing strength off electric field and gravitational force. So let's let's see how which is how strong is electric field. So electric field here is 5.58 times sent a letter to 11. So So let's let me approximate it, because in this question you don't have to actually solve it. So it's six times 10 power 11. You temper. Cool. Um, let's find the repulsive force between electrons force between electrons so e minus is equal to K Times Q squared, divided by distance square. So assume distances. Small approx. It's assuming art is one. Let's simplify the calculations. And Kay, you know, is 99 times and power nine times que square, which is electronic charge. Uh, I'm sorry, Mike. Computers is hanging. Okay, now, electronic charge this 1.6 times 10 power negative. 19. So square 1.6 in times to empower. Negative 19. In this case, that will be approximately two point five I'm approximating. So don't take this number kept accurately. 10. Foreign entity of 38 on DDE So this multiplication will result in answer, which is close to 20 times 10 power negative 29 Newton. Now let's calculate the gravitational force of attraction gravitational force because gravitational force is always attractive. Let's find out M e So myself, electron. I'm sorry about that myself. Electron times gravity. So in this case, we cannot use this question. We need to use the g times M e m e, divided by distance squared. So let's assume that electrons are the same distance are equal to one meter again. To simplify the calculation value of G. It is off the order of 10 power negative 11 which is seven times 10 Phone in what we believe in. Remember that I'm still approx are using approximate values. Massive electron is 9.11 times 10 power negative. 31 So squared off nine is 81. So I'm gonna use that times 10 power Negative. So 31 plus 31 in 62. Now all we have to do is multiply 81 time seven. That's where you give me some 5 66 5.6 times 10 power. So this is negative. 73. I'm making spy porn six or negative. 71 Newton's. So let's compare gravitational force with electric force. See that it's 10 power negative 1929 And this is 10 powerful negative 71. So you can say that gravitational force is very, very weak compared to electric electrostatic force of attraction or repulsion

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