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Now predict the motion of the swinging wire, if yOu turn the magnet around, s0 that the south pole is Up, keeping the direction of the current through the wire the ...

Question

Now predict the motion of the swinging wire, if yOu turn the magnet around, s0 that the south pole is Up, keeping the direction of the current through the wire the same aS in part b Answer the following questions:What is the approximate direction of the net magnelic field of the magnel near the wire? Explain your reasoning_Which direction_ if any. would the wire move? Record your prediction for the direction of motion of the wire Explain your reasoning for your choice of direction or explain why

Now predict the motion of the swinging wire, if yOu turn the magnet around, s0 that the south pole is Up, keeping the direction of the current through the wire the same aS in part b Answer the following questions: What is the approximate direction of the net magnelic field of the magnel near the wire? Explain your reasoning_ Which direction_ if any. would the wire move? Record your prediction for the direction of motion of the wire Explain your reasoning for your choice of direction or explain why it wouldn` move_ Carry out the experiment in part With the switch closed, bring the magnet up under the wire with the south pole up. Observe the direction of motion 0f the wire: Do not hold the switch down for long periods 0f time Or you will run down the battery quite quickly The motion may be small, but you will be able t0 see it. Record the direction ofthe motion Draw the direction ofthe field the direction of the current and the direction of the force on the wire in the picture below.



Answers

A wire, shown in Figure P17.48, moves downward perpendicular to a magnetic field.
(a) In what direction will the electrons in the wire move?
(b) After the electrons are forced in one direction, leaving positive charges behind, an $\vec{E}$ field and potential difference $\Delta V$ develop from one end of the wire to the other. The electrons no longer move, since the electric and magnetic forces exerted on them
balance. Show that this happens when the potential difference
from one end of the wire to the other is $\Delta V=v L B$ , where $v$ is
the speed of the wire, $L$ is its length, and $B$ is the magnitude of
the magnetic field. Describe two real-world situations where
this phenomenon might occur.

We have. Ah, currently there is produced in a wire that has some resistive ity. And we want to know the magnitude of the magnetic field at that point b doing toe the current that's passing through the wire in different times. So for a B and C, we want to know for a we want to know for the because many, many seconds or B, he was 40 minutes seconds. I foresee you want to know for 60 minutes, seconds and from the figure is not soaking in the sketch. But if you have the book you can follow, we're closing the figures. Chose that when we have t close to any second you have, the current goes for. So for this case E, it was for home Paris for this case, it goes eight, um, purse and in this case, a equals 10 of theirs. And then we can find the magnetic field be just Monsieur I over to buy our and this case, this zero point 089 dazzling you could test DNA and in this case, be people's view. Zero gain the same former to buy our and substance of the violence. Is this your point. Anything it does look. And in this case, the same formula. You zero, I write it I took by our in this case is you're going to to zero. That's love now, for part D. He left. We want to know the magnitude off the magnetic field at the point pay. Do it to the displacement current. So well, for this, we had that the displacement current is given by the variation elective field. That's so they're a the deity. And we have in this wire that the attic field is given by who I divided by a. So we get that displacement current is at slow zero row the identity where we have from the figure that the identity easy going, Toto under Empress for a second. So we have that the displacement curve the magnetic field Do the displacement current now at the same 0.24 in in 60 seconds. So let's do this. So this is for they he f is 20 minutes seconds. This is but in many seconds, 60 minutes seconds. And this use, uh B I equals zero in displacement divided by two pi r and there's this 6.4 times and man strain to Tesler here the same formula. And because the the current induced current is the same, we have the same driving 6.4 times and demands to Jasna. And for the this case, this is outside the current. So the current is already shut off. So there is no induce current on Lee, the the other current. So we have that be AII is equal to zero. No, now for by G and H, we want to know at the point B and 20 seconds. When is the direction off the magnetic field from the current and from the most current. So for by the right hand room we have the direction off B I is out of the fish and e at the same time Be I Day is also for age is out off the page. So we have the current moving here and then the magnetic field This coming straight out off the page

Inside the coil magnetic fields points to the right. As the magnet approaches, the vanity field increases. So manatee fields increases and points towards the right. So the current flows counterclockwise as as viewed from the right Oh, Lord to the right, in the Gabbana meter, through in the Gazal. So for part B, the magnetic field is still pointed the right but eighties increasing. So the current flows to the left through the gavel. Now, for the next two parts, we will have the current to be proportional to the number of turns current to be proportional to the number of voltage using these. If the voltage is chance to do V then the current oz. The changes from I to do I or it doubles if the bar magnet is held, not sowed and south north direction then from here, total magnetic filled. Our it was zero or total magnetic flux equals zero hands. The total government will videos you Zito and for the final barred both the situation gives same or similar rather result

In this problem on the topic of magnetism, we are shown in the figure the current that is produced by a wire of relativity, 1.6, 2 times 10 to the -8 or meters. The manager of the current versus time is shown in the next figure. The vertical axis in that figure is set by I. S. Which is 10 mps. And the horror horizontal axis scale is set by tears, which is 50 milliseconds. The point P. Is that a radio distance nine millimeters from the center of the wire? And we want to find the magnitude of the magnetic field B. I. At point P. Due to the actual current i in the wire firstly at 20 then 40 and then 60 milliseconds. Next, we'll assume that the electric field driving the current is confined to the wire. And we want to find the magnitude of the magnetic field. The idea point P, which is due to the displacement current in the wire again at 2040 and 60 milliseconds. And then we want to find a 20 seconds the direction of B. I. And B. I. D. Now from the figure we can see that I. Is equal 24 mps. When the time T. Is 20 milliseconds. And so from here, the magnetic field due to the actual current B. I. Is you're not I over two pi R. And using the information given this is zero point zero 89 millie Tesla's. Yeah. Next. If we are given. Yeah. The time of 40 milliseconds. The current is eight piers. And so using the equation above, we get the magnetic field B. I. To be 0.18 molly Tesla cars. Yeah. And then for part C. We have at 60 milliseconds. The current I. is equal to 10 and piers since the current is 10 mps. When T is greater than 50 milliseconds, which means that the displacement current or rather the magnetic field B. I. Is equal to 0.22 molly Tesla's now for part D. The displacement current, in terms of the time drought of the electric field, I. D. Is equal to absolutely not A. D. E. D. T. Yeah. Yeah. And the electric field E. Can be written as the resistive. Itty role times I over A. And this is in terms of the real current. And so therefore the displacement current I. D. Can be written as absolutely not times row time's D. I. D. T. Now for a time of less than 50 milliseconds we have from the graph that D. I. D. T. Is equal to 200 mps per second. And so therefore the magnetic field due to the displacement current B. I. D. Is equal to mu note i. d. over two pi r. And this is 6.4 Times 10 to the -22 kessler's for part E. As we've done in B, we find the I. D. Is you note I'D Over two Pi R. Which is 6.4 Times 10 to the -22. Okay, Tesla's for part F. Yeah. Yeah. We have the I. D. T. Is equal to zero. And so we can see that by the reasoning we've done before the magnetic field, B. I. D. Is equal to zero. Okay, next. For part G. We can use the right hand rule to find the direction of B. I. And so at T. is equal to send 20 seconds be I. Is out of the page And at T. is equal to 20 seconds. The magnetic field due to the displacement current B. I. D. Is also out of the page.

The force accepted by the magnetic field is given by I Times and Crosby on. So the magnitude of the force is going to be a i l b time sign Find their fires. The end of the Ellen B on the direction off is given by right Kendall being applied on the length off the direction off the floor off current on the magnetic field. Direction now for the wire to ribbon addressed the net force on the wire Should be syrup. That is the force exerted on it on the wire by the magnetic field Must have the component directed up the incline. So like that. So there should be a component off magnetic field along this direction. How to produce a force in this direction. The current on the wire must be directed from left from right to left in the figure. The problem in the textbook are viewing the wire from its left hand on and from the left hand, the direction should be as shown over here. So this is the image off the wire from its left hand. I So we have a magnetic seed, a competent off my medic food awkward so that there is a competent off magnetic field along the direction off, implying on DH forces here on DSS occurring must be directed from left to right. So sad from right to left. So that is that should be like this. So current going from this angle, the current should be coming out off the laying off the screen. So we dropped three. That body diagram off. Ah, this, uh, why off the for the wire. So this is the free body diagram that have already drawn. So basically buying ah, is the direction off the incline upward on exes? Perpendicular to that, an ex points positive ixis town work. Andi, Since f i points, he'll we have components along x and y direction. And similarly for md it is the gravitational force. And since the Net force on the line here in Seattle underwire to be addressed, we should have f submission off If y to be called zero on. Yeah, basically that we should also have some mission off f X to be equal to zero. But as you can see, FX bull fixed consist off all the forces along the positive ex direction. So to counteract that we have the normal force, the contact force from the plane off tent line. So this is going to be s I sign Rita less empty, caustic down. So these two forces minus and because this is in the opposite direction is equal to zero. But we basically don't need the normal force here, so we can just ignore doing this Ted doing this calculation. So we go with the net force along my direction, Tau zero. And this gives if I caused the savages and positive my direction minus M design puta minus sign is because, and designed to the points in the opposite direction to this force. And that should be going to zero. And this gives are fine. Okay, So before doing that, less that persist, use the value ofthe force. The question off this force to with this, because forces basically the magnetic force somewhere. When I used this equation, Dimes costed down minus in design. Tick tock, constancy pants. Since the angle between Ellen be the current direction off current on the magnetic field, as you can see here it's 90 degree, so sign files. Basically one. Still, they question reduces toe this. Now we can solve this equation and we get high to be equal to mg B time's scientific over costume. And we know that scientist over cost it. I stand it us. So I insecure, too, and you can take over one times the Latin dude off magnetic field.


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