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Question 71 ptsIn some region of space the electric field is given to be E = 12x?i where 12 has appropriate Sl units. What is the potential difference between %i 0 ...

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Question 71 ptsIn some region of space the electric field is given to be E = 12x?i where 12 has appropriate Sl units. What is the potential difference between %i 0 m and Tf 4 m?Question 81 pts

Question 7 1 pts In some region of space the electric field is given to be E = 12x?i where 12 has appropriate Sl units. What is the potential difference between %i 0 m and Tf 4 m? Question 8 1 pts



Answers

An electric field $\vec{E}=(\vec{i} 20+\vec{j} 30) \mathrm{N} \mathrm{C}^{-1}$ exists in the space. If the potential at the origin is taken to be zero, find the potential at $(2 \mathrm{~m}, 2 \mathrm{~m})$.

In this problem we have to find the potential difference where electric field and initial and final position of the two points are given. So for party, the electric field E. Is equal to 20 Newton curriculum. I can because it is a long positive X axis and the displacement is operation victor of b minus patient vector of uh huh. Person later of B is for I plus do J zero. For a. So displacement is for I plus to jail has changing potential difference is equal to minus E. Dot delta are 20 I camp dot four. I plus to Jacob. So I kept dot product with icap will be one and it will be minus 20 into four. I kept output out. I can and I kept dot product with Jacob will be zero so it would be simply zero. So this is -80 vault for part B. And displacement is Persian victor of BS six. I plus five J. Position vector of a. is for I plus two J. So this is equal to do I plus T. J. So potential differences Yeah minus a. Don't tell to our called minus 20 I kept dot do I cab plus Jacob This will be equal to -20. I kept sorry 20 into I kept I kept bless sorry minus 20 Into. three. kept. I just continue to is 40 minus 40 and Icap dot icap is one so it will be simply minus 40 and 20-3060 but I kept out Jacob is zero So this is -40 vote for part C. The displacement is mhm position vector of b minus position to be is six. I cab plus five. Jacob minus zero equal to six I cab plus five Jacob. So electric field is sorry potential difference BB minus V is equal to minus e dot delta. Going to -20. I can .6 I cab plus five Jacob. This will be called -20-6 cap. I don't like minus 25 I kept Jacob. So this will be zero due to I don t J and it will be -20 into six equal to minus 20 involved. So this is a potential difference for park six. Now the relation between the answers of parts A B and C is that potential difference for part C is some of potential difference of parts A plus potential difference of part B. Mhm. So this completes the solution. Thank you.

In this problem we have a given electric field and we have to find out the potential at origin where potential at 0.10 m comma to meter is given. So we know that TV is equal to -1 dot dll Davey is changing potential and er is the displacement infinitely small displacement and is electric field No, D r is equal to dx I kept plus Dy Jacob. So E dot dear will be equal to he is ex I kept given dot dx icap plus. Do you weigh Jacob? So this will be X dx and I kept multiplied by Jacob will be zero. So you dot drd? It's simply X dx. So we have DV equal to x dx minus x dx. No, we integrate on both sides. So the potential will be integrated from the potential act origin to potential at B and X varies from origin two. The x coordinate of the given point which is 10 m. So on the left hand side we have vp minus vo equal to minus a 0 to 10 X. Dx. Now V. P. Is the potential act The given point which is 0- potential at origin video equal to minus a access square upon to zero to attend. So we have not equal to a Turn. The square of 12 find necesito And value of a. is 10 involved. four m square into tennis square upon to Is equal to 500 fault. So this is the potential at origin and this completes the solution. Thank you.

Hello for problems, 16.36 We are asked to find the distance of a charge from a point p. We know that the electric field at Point P is just equal to zero. Because of this, we then can say that the electric field, due to charge one, is going to be equal to the electric field due to charge to charge Q one charge Q. Two. In addition, we are told that we we are not told. We can see that Charge one is equal to charge q two divided by two. Thus, we can start figuring out what our electric fields are. To do this, we can use the equation. Electric field is equal to k que over r squared. Thus it is going to be equal to que que won over x squared that must equal que que to all over x plus our quantity squared. Simplifying this equation out, we can come out and see that X squared must equal Q one over Q two times X plus our quantity squared. Substituting in that queue that Q one is equal to Q 2/2 week Now can come up that X squared is equal to X plus our quantity squared all divided by two. When we multiply and simplify this this out we come up that X squared minus to X r minus R squared equals zero. We can use the quadratic equation minus B plus or minus the square root of B squared minus four a. C all over to two. Factor this equation out. We're then told once we used the quadratic equation that X is going to be equal to are times the quantity one plus or minus the square root of two. Since the X in this direction here cannot be negative, we know we just have to look at the positive value of this. Thus, X is equal to our times. One plus the square root of two or X is equal to 28.9 centimeters.

So as we see here in this diagram, we have point P, which is this black dot and then, uh, the charges are those red doors with their key want youto Q three and Q four and the distance between the black dog and you want youto cute three is D and the distance from P to queue for a studio. Also, we're given that Kyu won and cute, you are equal Where que tree is positive fight. If was it a three and Q four is negative? Well, the he means the charge of Elektra. Also, the distance is given us five micrometer. So first of all, when we have a problem like this, it's always better to actually specify the access so that we can. I understand the problem better. So, for example, in our kiss since peas at origin. So let's considered that as our origin of the Korean system and ah, the dude and frumpy to queue for we consider the direction as why experts so from P to queue for is the direction for why access? So we call it why and ah, then the perpendicular direction toe why access is only X axis, which is a long queue for and cute, too. So let's call this positive X. So we have positive X perpendicular is perpendicular it away Now. That means if we look at the X axis, for example, we see that we have a point here, and it's always better to consider this point as one unit charge. It's ah like, for example, we don't, um it's easy to visualize if we actually place a pseudo charge here, which actually doesn't have any charge. But it's just to visualize how the electric fields are working. So, for example, we're considering, ah, positive unit charge is at center p so cute to his positive, and Q one is positive as well. So that means Q one will be pushing this for the charge along at what's Q two. Similarly cuter will be pushing the charge towards Kyu won. And since they have the equal number of charge, so the force will be equal and so is the electric field. So the electric field between the point two Q one is same as electric field from 0.2 cute, so that will be zero. So if we call you want for Kyu won and E two for you two. So Hee won is equal to E. To where, UH, this line represents the absolute value, so that means they will cancel each other so there's no force along X X axis. Now what about the wide reaction? So we see that in the wind direction. If this is positive and country is positive, so cute, you will tend to push the charge along negative y axis. But then we have careful, which will try to pull the charge because it's negative and door dis positive year. So it will try to pull the charge along positive direction so we can actually look for the electric field and see what the Net electric field is. So let's let's say Q three has electric field eatery and Q four has E four, so the Net electric field in it music will do one by four pi. Absolutely not. Uh, that's actually shifted to the bottom so that we have more space to work with. And then we have Q four, which is the magnitude will just take the magnitude and then it's toe. He's quit, and then we subtract that from Q Tree. Since the science are opposite, so this will be huge. Three. Divided by D squared And since it's in, Why direction? We just put jihad? Jihad is the union factor along my objection, So this will give us one by four by and Sylar Not, and then Q four is 12 e. So that's 12 e right here on DA. Then we divide that by for B squared. And then we subtract that from Q three, which is three. He divide that by the squid, and then we have Jake direction. And as we see here, this is three. So the positive and and so three by D squared can be cancer loud because we have a negative sign here, so that keeps a zero. So the total electric field at the origin P is it's, you know? All right. Thanks for watching


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