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(50) %) Problem 2: One half of rigid rod contains uniform net positive charge whilc thc othcr half contains uniform nct ncgativc chargc as shown in thc figurc _ Thi...

Question

(50) %) Problem 2: One half of rigid rod contains uniform net positive charge whilc thc othcr half contains uniform nct ncgativc chargc as shown in thc figurc _ This system is an clectric dipole. This electric dipole is then placed in uniform electric field of magnitude 25 NIC,as shown in the figure _E+QLI2Li2If L= 25 cm and Q = 7 nC,what is thc magnitudc of the torque (in nN:m) cxcrted 0n the clectric dipolc by thc clcctric ficld? Gradc Summary Tnet 10.91 Deductions 0%6

(50) %) Problem 2: One half of rigid rod contains uniform net positive charge whilc thc othcr half contains uniform nct ncgativc chargc as shown in thc figurc _ This system is an clectric dipole. This electric dipole is then placed in uniform electric field of magnitude 25 NIC,as shown in the figure _ E +Q LI2 Li2 If L= 25 cm and Q = 7 nC,what is thc magnitudc of the torque (in nN:m) cxcrted 0n the clectric dipolc by thc clcctric ficld? Gradc Summary Tnet 10.91 Deductions 0%6



Answers

$\bullet$ $\bullet$ Torque and force on a
dipole. An electric dipole is in
a uniform external electric field
$\vec{E}$ as shown in Figure 17.49 .
(a) What is the net force this
field exerts on the dipole?
(b) Find the orientations of the
dipole for which the torque on
it about an axis through its center perpendicular to the plane
of the figure is zero. (c) Which of the orientations in part (b) is
stable, and which is unstable? (Hint: Consider a small dis-
placement away from the equilibrium position, and see what
happens. (d) Show that, for the stable orientation in part
(c), the dipole's own electric field opposes the external field
for points between the charges.

So here were given the magnitude of the charges and the distance between them, which is what we'll need for part A to find a disciple moment. So we're going to use the equation. P equals Q times D. We plug in our values that were given in the problem. You find that the dipole moment is equal to 1.4 times 10 to minus 11. Cool, OEMs times meters. And as for the direction, the direction of the dipole moment is always from the negative charge to the positive charge. And so if this is our negative charge and this is a positive charge, this is the direction of the dipole moment. Now, for Part B will also need the torque and the angle between the electric field and the line connecting the charges. And so the equation we're going to use here is torque is equal to dipole moment times the electric field times sine of the angle that were given and we want to solve for the electric field here and so we can write. The electric field is equal to torque over the dipole moment times sign of our angle. And then if we plug in our values were given for the torque and the angle and the dipole moment we got from part A. You find that the electric field is equal to 860 Newton's over Kulov's.

For a problem. 63 were given. Q one Q two, which is negative. 4.5 Nana Holland and four point by Nana. Column At a distance off 3.1 millimeter. So what he needs toe find the electric dipole moment. The electric diaper moment. She was, too. The church times the distance, which would, which would give us 4.5 Senate restore the negative nine with deployed by 3.1 times, then raced to the negative three. So the electric level moment equals to 1.4 times 10 raced through the negative 11 column meter strong, negative to the positive, and for B were given a dark, which is it was to 7.2 times 10 threes, too. The negative name you told meter. So this is the heart. And then Angelus, Curtis explained, nine degrees. So where to find the electric field, which this die police in. So our formula would be for Sequels to the right point, multiplied by the electric field, dictated by sign of data. So substituting our value, he had win for attention and they swept the negative 11. The unknown electric field say enough 36 point name. Our electric field is equal to a 56 point 54 you turn for calling

Net force as a victor equals If it's it said thus if Why White hat Your fix is you yet by s Cube yet? It's, uh thus if why is you you I minus you. You are Why had 10 So the man forces sealed nor it was Don't give you the negative charge. Ron, Talk with a positive charge. We were about to be negative. You guys e guys, do you learn to scientific data? Yes. You translated E that you were too scientific. It was negative. You e b signed it up. So putting the numbers in, we would have negative screen time. Stand to the negative six with all these e electricity is two times 10 to the minus four. You don't part for them. B 0.7 times scientific data sequins. So for different values off PETA began Find the dog. So Tetteh was a star for zero degree We have got zero dark born 6.9 Big me. We have got negative 0.0 who five knew done by meter star And for 1980 we have like the maximum 0.0 for two. They don't need a major dog on the unit Authorities needed

So let's first drug charges. So we have judge Q one that is negative for Point fire. Mana Coghlan's the hand. This is the circuit somewhere over here. Then we have judge Kyoto that it was positive for 0.5 mana pool rooms on the distance between those two charges. As let's call back a so administrate that in another color so that is a on is given to be three point fun trip 3.0.1. Well, let me go andan standard units. This is a cult. Is it a point? C 00 31 meters Now the electric field is said Don't be making an added Tita the the lying joining these two charges on dhe Tita is given Toby 36.9 degrees. Now, in the first part, we have to find the electric type of moment that would be on that is cross product off, not girls product. Sorry. Um, the magnitude off the charge times the distance between them and here The magnitude is feudal times. Hey, on. And by deploying the multiplying the judge times the distance between the truth. John, just be fine, though. Lecter diaper moment to have a magnitude 1.395 Dying stained with the blood Linus 11 Meet Dutch and is this is in centimeter. I have already done the concussion. Now this is just the mic me dude. Now direction since this is a di Poole and hence the magnetic type of movement. So the electric type of moment on DDE in a disciple, the direction off the type of moment All these points from the negative charge towards the positive judge Hence the direction off this victor be iss from q one. Hope you too on Duh. This is along the lying joining these two judges. And if we say that this is the positive X axis, this is the posture y axis and has this is the negative Except it sex is so we can say that effect a p is in the positive x axis. Since we can write, I cap over here So that's a magnitude and direction off the electric type of moment. Now in the second part Oh, you have to find the electric field. So the angle between the electric field on DDE no electric type of moment iss Tita Since the type of woman points towards the positive X axis. So the angle between these two is the state, and that is going to be 36.9 Degree on dhe talk on the Styx pole is has a magnitude be dines e giants Sign Tita on this dog is given to have a magnitude to be called to 7.2 times 10 to the Bard minus nine New turn times meter and this is given in the problem. So by this, using the secretion, we can find the electric field, so even be equal to 7.2 times, then the bond minus nine New Think Tang's meeting over magnitude off the Piper moment. Dimes scientific not substituting these two values and doing the calculations. We get the magnitude off the electrical Victor Toby 3 59 blind 61 Newton Bakula. Now, your answer might come out to be a little bit different from my in depending on how much approximation you have taken. For example, if you approximate or this to be 1.4, then this answer will come onto legal toe 8 56 I'll find something So yeah, What a ride just depends on how further you go on making the approximation. So yeah, the this is the magnitude off the electric field on it, in the direction is already given. The direction is like 30 degrees, 36.9 degree from ex Texas. Thank you.


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