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A train is moving directly south with a speed of 10 m/s. If the downward vertical component of the Earth's magnetic field is 5.4 X 10-5 T, find magnitude and d...

Question

A train is moving directly south with a speed of 10 m/s. If the downward vertical component of the Earth's magnetic field is 5.4 X 10-5 T, find magnitude and direction of the EMF induced in the rail car axle 1.2 m long: (For the direction, show which side of the axle is positive and which side is negative).

A train is moving directly south with a speed of 10 m/s. If the downward vertical component of the Earth's magnetic field is 5.4 X 10-5 T, find magnitude and direction of the EMF induced in the rail car axle 1.2 m long: (For the direction, show which side of the axle is positive and which side is negative).



Answers

A train is moving directly south at a constant speed of $10 \mathrm{~m} / \mathrm{s}$. If the downward vertical component of the Earth's magnetic field is $0.54 \mathrm{G}$, compute the magnitude and direction of the emf induced in a rail car axle $1.2 \mathrm{~m}$ long.

For this example. We're trying to determine what the induced emotionally MF is in a car. Given that the car is traveling forward at 25 meters per second, it has a with of two meters and the magnetic field pointing downward or into the page. In this case, it's 4.8 times 10 to the fifth test. Less so to do this, we're just gonna remember that since all of these vectors are perpendicular to each other, that is the width of the car, the velocity and the, um and that Did you since also say all those things were perpendicular? We can just use the equation for the emotional Yemen in a metal bar in a constant magnetic field, which is the Times B times L where in this case, R l is going to be our whip. So v times be tons w for us, and I'll be specifically the component of the magnetic field pointing into the page. So since we knew that our job here is as easy as just putting on in all our values into that equation, if we do that, we will get that the induced in that is equal. Teoh 0.24 Bulls or, if we moved place back once in those three times will be 2.4 times 10 to the minus three bolts. Now, let's consider the polarity of the car. So where the where the charges were gonna be on the car. So we're just gonna use the right hand rule to figure this out. So if we point our thumb in the direction of the velocity and then our fingers on a right hand in the direction of the field, our palm will go in the direction that the positive charges will be forced to. So if that's the case, he will be up like this. B will be into the page like this. And the force is going to be to the left like this for positive charges, right? Negative ones will go to the other side, so of where ins. And if we're the U. S, then it's gonna go towards the driver's side of this car or the left. So we'll say the driver's side slash left side is positive. There we go. We just calculated the emotional MF induced in a moving car and we also determined with the polarity of that car, would be given the are using the right hand roll

Hi and a given problem. Land of horizontal wire which is falling vertically down which the length is given as 0.8 metre and it's for equal velocity. That is given as we is equal to fight meter per second magnetic field here is given as 1.1 Tesla and it is directed from East two. This to suppose if this is the direction of magnetic field from east to west there, this will be, this is not and this is south and this is the wire which will be lying in north south direction and it is falling down like this, the velocity V. So first of all, we find the magnitude of emotional EMF induced across the ends of this fire. So emotional IMF Hindus across the ends of the wire is Absalon is equal to the product of magnetic field with the velocity and with the land. So here it will be 1.1 Tesla multiplied by five m per second, multiplied by 0.8 m. So finally the magnet you love. This. EMF induced comes out to be 4.4 world, which becomes one of the answer for this given problem. Now we have to find which end of this wire will be at higher potential for which we will use lemmings, right and rule, which is a rule to find the direction of currently in use in a wire. Then it intersects the magnetic field lines for particularly. And using that rule, we've come to know the direction of current induced in this wire as a result of this emotional you have induced that is from south to north means in the diagram it will be like this now, as we know in case of induced current in a while, his current induced in the wild is from it should be from low potential to high potential as this wire will start behaving like a source of e. M. F. And within, the source of the current always runs from low potential to high potential. Hence, we conclude its north end will be positive as compared with south end, which becomes another answer for this given problem. Thank you.

Question number 14 If what train is moving towards left with every loss TV, this velocity, we is considered as negative by sign convention. And it is given that this train is stops after some time. So the ex elation should be in the right direction. Order. Was it that action? Because the X elation should be in the opposite direction off the initial velocity to stop the train.

Huh Of a value I equal to 15 amperes directed along the positive X axis So we can put this in the X that direction and then we also have a force per length or F over l of 0.12 Newtons per meter and that is in the negative white hat direction were asked to calculate the magnitude and direction of the magnetic field in this region. So the force from the magnetic field in this region f is equal to the value of the magnetic field be times l times the current times, the sine of the angle between the current and the um, the direction of the length of the wire data. A favor here is equal to 90 degrees. So therefore we can conclude that the force is equal to be times l a times I rearranging too soft for B We find that the magnetic field B is equal to fo ver el, which was given in the beginning, multiplied by one over I which was also given them the beginning. Okay, so this gives us a value equal to 8.0 times 10 to the minus three Tesla. You can also wrote eight Millie test level. We'll just leave it in units of Tesla. And then the next thing asked his direction, Alec, Well, we can use the right hand rule toe find the directionality. And, uh, of course, just using a simple X y see access. So we have X. We can call this negative. Why? So if you point your index finger in the direction and we'll call this see if you point your index finger in the direction of the, um, current, you point your middle finger in the direction of the the force over length F over L, which is negative white hat. And then your thumb will point in the direction of the magnetic field so that if you look at this, if you put your finger along X if you put your index next finger along X, your middle finger alone, why and then check the direction of your thumb. Using the right hand rule, we find this thumb points in the positive see hat direction so we can say the directionality here, Izzy hat. And since it has magnitude and direction weaken Sebi is a vector. We'll box the scent is our solution to the question


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