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Problem 4 (20 points) Determine the magnitude and direction of the magnetic field at point P if I=4A a= 20 cm and b= 100 cm...

Question

Problem 4 (20 points) Determine the magnitude and direction of the magnetic field at point P if I=4A a= 20 cm and b= 100 cm

Problem 4 (20 points) Determine the magnitude and direction of the magnetic field at point P if I=4A a= 20 cm and b= 100 cm



Answers

Find the magnitude and direction of the magnetic field $\vec{B}$ at point $P$ in Fig. $30-32$, for $|i|=10 \mathrm{~A}$ and $a=8.0 \mathrm{~cm} .$ (See Problems and 16.)

So basically, we have a real job shape in which we're currently following. I want to find out, manipulated in cuba. So sleep. You look like this one like. Yeah, this is the same. Even if I'm any different at this point. Okay. And coral currently following in and ecology by direct and that means in this direction. And this is point over helping to find the men in the field. Side length is two. And this is a. Okay. So basically this is too this is too this is a resident when we. So what we need to find is that made the field uh we'll find the magnetic field. That point me very simple question. What we can do it uh since it is in the uh anti clockwise direction, currently is in the anti clockwise direction. So we know that the mind if you do this five, this one since this virus passing through this point itself. So this will be because you know, only that look this. What will we do? We're different. We only do this man and this man this man. And if you look at the point where we uh into this way the field will be what P. Will be outside the plane. So let me try this just point. And due to this way this will be also outside the plane. And due to this way this will be inside the plane And the 21 more by this man uh that we in the inside of land. So these two were indicated the outside the plane. These two were inside the balance let's say doctor. Well jim anything. Just we're presuming that uh inside the plane is positive. The only thing that's listed in santa. But it's pretty bad. So that means to me in it that will be anything. But due to this guy that will be mean or I afford for I. D. And to do this one this revolution we already know because the other the same demonstrated the same questions so two times off one in the Algerian Society send you that we still and plus of this single How do you do this to to send it to this one the department regularly about this. Yes piracy is able to obviously this is this is equal to we can see and the energy that 45.2 and this will be an original I can inside the plane. Okay and if it is outside the buildings I can only two times of me you know I on four piles and over here the perpendicular distance was and all from hell perpendicular distance uh to into No one wanted idea and the second one will be too and that will start 45 years. You haven't gone through that. So it will be No, you know, I only two times considered. So to go to buy a minus off These two and to the council also from New York. Hi on. Mhm. To this, To this poor route to into why. Yeah. So the final magnetic field over there, that will be so it will come minus of, you know, I want to buy able to route to I referral to buy an in the direction of uh inside the plane. Okay?

Okay, so this is a fun, conceptual problem here, So I have a couple things written already. So I have the magnetic field were given in two directions. One of the directions is in the negative y component. The other one is in the positive x component. Then we have in blue. We have the velocity of the particle traveling in the positive Z component. So this is what it would look like in three dimensions. Um, three dimensions gonna be something that can be sometimes little bit difficult to conceptualize. But imagine this X axis as coming out off the page at NZ. And why are the planes of the page so you can imagine the negative X direction would go into the page this way, and then Z would just continue down her negative z. So this isn't three dimensional space. We want to find the magnetic force at a location here. It could be anywhere along this blue line here. We're just gonna make it right here for simplicity. Doesn't so much matter the distance for what we're trying to calculate. So we want the force here. So you have two components of force now that are affecting that location. One here from this component of the magnetic field and one here. So this is coming up towards it. And this is coming to the right diagonally. So we'll need to do to separate equations so we'll do the math over here. So to get force we used the equation. F is equal to the magnetic field times the charge times the velocity. Now this typically has a sine of the angle between the force and the velocity. But as we can see all three directions here, both red arrows and the blue arrow are all perpendicular to each other, where this is the right angle and this is a right angle. So it will be sign of 90 degrees or sign of pi over two in radiance, which is just one. So we don't need to keep that into consideration here. So this is the 1st 1 I will say this is from the one in the positive will call positive X direction F one and the negative y direction. F two f twos. Negative. Y F one is positive x So for the positive extraction plugging in, we have the values for B Q and V plugging all of those in. We find that this force is equal to 0.0 four, and it's important to note. Everything we're given is 22 significant figures. So we'll want to keep the zero. Um, everything is in S I units, so we'll be in Newton's here. You can also write this in scientific notation. As for we want to keep zero zero is accurate, so it needs to stay there. Um, this is times 10 to the minus third, and that's the force from the positive X direction component of the magnetic field in Newton's. So we'll need to do it again, for part are for the, uh, the second part of a magnetic field F two same equation. Same thing, just different numbers. Plugging those numbers and you'll get 5.5 times 10 to the minus. Three exact same process is the 1st 1 but these air in two different directions. So now what will want to do is go and look and see what direction this force will be in. That means we get to use the handy, dandy bright hand rule. So let's go back and look at F one to start. So we have a force using the right hand rule. You want the force to be your middle finger or your palm, depending on which version of the right hand rule you're using. So typically, I like to start point my pointer finger in the direction of the magnetic field, which would be the red arrow here. So that's your pointer finger, your thumb. You want to go in the direction of the velocity, which is the blue arrow. So right now, your hand should kind of look like a gun symbol. You have your pointer finger pointed out in the negative X direction and your thumb pointing up in the Z direction. Now, if you point your middle finger the direction your palm is facing so all three fingers are perpendicular to each other. It's gonna point straight out this way, which means that for F one, our force is in the positive X direction. Or if you have experience with vectors, this would be inthe e positive. I hat direction, the unit vector I. But we can just say it's in the positive extraction here. If you don't have any vector experience. No, I'm sorry. That's for f one not have to. So F one is in the positive extraction or I had because this is three dimensional space. You really need to keep track of your directions are very important, especially for equations like this, where you have three different variables that are all pointing perpendicular to each other. So thats F one. So I'm gonna draw the force in green. That's at this point here. So that's pointing out this way. Same direction is the X Axis raid. At this point or any point along this blue line, it will be pointing in the same direction. Now let's go look at F two. I'm sorry. That was for F two. I did have to on accident. So we'll right, that is f to you. F two is in the positive extraction. This is why labeling things can be really important and help you from getting a little confused. So that was for F two. The pointer finger should be along the magnetic field, which is what I did for F two. Now for F one, it's pointing out. So you want your pointer finger to be pointing straight towards yourself and your thumb along the Blue Arrow here for F one. So we have pointer finger in this direction thumb pointing up in the Z direction. And once again, the direction your palm is facing. Point your middle middle finger that way, and that'll point this way. So your your three fingers. In this case, this should be your thumb. This would be your pointer finger, and then your middle finger will point this way. You kind of have to twist your right hand around to get it to do that, but it's important that use your right hand. Does your left hand will give you the reverse? Or, if you had a what you would get if you had a negative charge. So these year, three fingers. So in this case for F, this is F one. Now F one is pointing in the positive y direction, So if one it's positive why, Okay, so we have to force components at this location. We want to find the magnitude of the total force on this point. So the magnitude there's a formula for finding the magnitude. Um, you can also make a triangle and use the Pythagorean identity or the Pythagorean theorem. We have doodle here we have two triangles. Are we have one triangle? Two lines. This WAAS double check. That was It's labeled Al appear again. So this one was the positive X direction was from F two. So this was F two. The positive y direction was from F one just to keep them straight. So we have f to here, and then this is a right angle for F one. So now this makes it a right triangle. If you connect here to here, and we have each side here, um so to find what this value is here used Pythagorean theorem, which is this quantity that we found. All right out for you. So you have called this. See, this is B. And this is a I figure in the're, um, says that c squared is equal to b squared, plus a squared or a squared plus B squared. It doesn't matter what order you put them in. So we want to find C in this case. So to find. See, just take the square root of that B squared plus B squared. So it's the square root of our answers. We found for the forces squared. This is also the distance formula. This is where the distance formula comes from. It's the distance between two points, so you can use the same thing as well. Um, so this will This will be your be. And this will be your A. Put those into this equation and you'll get this is these are all in Newton's. You'll get 6.8 times 10 to the minus third. This is a Newton's. Okay, that is the magnitude off the force from both of these components here. And now, looking back at our diagram, we have that will be something. So it's from this force in this force. Both of those will push it kind of in this direction, the stronger of the two F two will kind of take over and soda lean slightly more this way. But we can find out exactly what that angle is by going back to our triangle we have here. So we have in geometrical terms. We have each of the two legs, and so a and B of the two legs see is the hypotheses. So if we want to find so what we're looking for is that the angle of the force to the velocity. So we want this angle now to find that you just take the inverse tangent of a and B, Or in this case, F one F two. So what we want to do here, let's make some space. We want to take the inverse tangent, which gives you an angle of F one F two, the force from F one. Do the force from F two on. This is something you can just plug right into your calculator. This gives you an angle data in degrees. You should get 36 degrees from that from your two numbers for both forces on there you have it. Your two numbers you have here the magnitude of the force 6.8 times tend to the third. And your angle. This is at 36 degrees. Now you have it.

Hi. And this given problem, there is a magnetic field which is being represented by the magnetic field lines like this. And it is clear that this magnetic clearly is going on increasing as the relative strength of a magnetic field is given by the gap between the magnetic field lines and here the gap is going on increasing. So the magnetic really stand is going on decreasing the point at which we have to draw the vectors for the magnetic field directions. These are yeah, this is point A. Then here this is point B. Then the point C. And here this is point B. And finally this is wind. E. First of all the vectors to represent their direction of magnetic field or E. It will be engine. This magnetic field line at B. This is the direction and as the magnetic field is less in magnitude. So the length of arrow should be a little less. Then it points the right land more or less then act going to be direction is this Tangential Again? & 8.8. Yes. No. Using the concept. Yes. The strength of magnetic field depends inversely on the gap between the field lines. So we conclude magnetic field is the strongest at point A which is more than that at B. As the gap between the magnetic field lines is going on increasing than it is more than that. Fc which is further more than that at D. And finally this is more than and yeah, There is one more point F. So yeah, this is point Mhm. At which the direction is this and the least magnetically will be there. So VD is more than that at E and finally, B. E is more than that. At means the magnetic field is least at point F And maximum at .8. So this is the answer for that given problem here. Thank you.

High In the given problem, there are two straight conductors. This is the lower one carrying a current I having a magnitude off N m Pierre towards right and above it another wire carrying the current. I having the same magnitude off 10 impure in downward direction. And the gap between these two wires is given as 10 centimeter. So the gap between these two wives is in senti meter. We have to find the net magnetic field in a magnitude in end in direction and a wind halfway between them. So the point will be better. It stands off, are by two means five centimeters or we can say five into 10. Dish one minus 2 m from both the virus. No, if we look for the directions off magnetic fields, do you do the individual wires for this horizontal wire? The direction off magnetic field at a point above it will be in our downward direction means like this. This is the direction off magnetic field due to this horizontal wire. Similarly, the direction off magnetic field at the same point Do do this vertical wire using right hand jungle again will be two words, right? So this is the magnetic field due to the vertical while So the net magnetic creed We be found by vector son off these two magnetic fields. No using by it and sever slot magnetically. Do you do ah, straight conductor off infinite land at any point, the stands are from the wire is given as you not by four by into do I buy our as the current is saying in both the wires and distance off observation point, it's same is also saying from both the wires so the two magnetic fields B one and B two will be the same in magnitude. So this is given as the value off. Do not account for Pike. This is 10 for minus seven, Tesla meter for NPR, multiplied by two in tow 10 and fear for the current. And for the stance. This is five into 10 departments to meter. So canceling the similar units meter by meter MPR by MPR and then this is five boozer 10. So finally this value off Beaven and be too comes out to be four into 10 to the power minus fine Tesla. So the net magnetic field using data go restaurant the net magnetic field will be found. He is five into 10. Dish part minus five in two rue to Tesla. As we know, the net magnetically will be the one e squared plus B two square square. Root off these two squash, so if you put the values of Given and veto, both are having the same value. So it becomes twice off, even inspired. Or we can say this despise off 16 into 10 dish for my understanding. Tesla So 16 intended for minus tent comes out as pour into tennis for minus five, leaving behind too. So here finally, the magnitude of this magnetically comes out to be 5.7 into 10. Dish par minus five. Tesla. This is the answer for the magnetic field magnet. You look magnetically and its direction is as shown in the figure. Thank you.


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