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Top: viewtwo coaxial solenoidsb...

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Top: viewtwo coaxial solenoidsb

top: view two coaxial solenoids b



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Two coaxial solenoids are made by winding thin insulated wire over a pipe of cross-sectional area $A=10 \mathrm{~cm}^{2}$ and length $=20 \mathrm{~cm} .$ If one of the solenoid has 300 turns and the other 400 turns, their mutual inductance is $\left(\mu_{0}=4 \pi \times 10^{-7} \mathrm{Tm} \mathrm{A}^{-1}\right) \quad[\mathbf (A) $2.4 \pi \times 10^{-5} \mathrm{H}$ (B) $4.8 \pi \times 10^{-4} \mathrm{H}$ (C) $4.8 \pi \times 10^{-5} \mathrm{H}$ (D) $2.4 \pi \times 10^{-4} \mathrm{H}$

High in the given problems. There are two solid noise having the same land and and the same radios. Ah which are around on the same core. The current passing through the first solid night is varying with the time as I want t is equal to I am into sign Oh my God! So magnetic field as a function of time lean with the first girl First solenoid will be given by B one is equal to me not and I where n is the number of turns But in England So here this is new not, and one the total number of turns in the first coil and smaller the length of the solenoid into I won d no, the flags has the same magnetic field will be linked through the second coil also so the magnetic flux to link through the second coil linked through the second coil second solenoid The total magnetic flux will be 52 is equal to the total number of turns in the second coil magnetic field induced to the primary coil and area of the second coil. So here it comes out to be and to into for b one this is a new note and one by L into I won deep and for area. This is by our square. No, we will put the expression for Ivan tea. So here it becomes new note and one and two by l into I am sign Omega t into by our square. We can see this is do not in two pi r Square and one and two I am divided by L into Sign Omega, which becomes the answer for the first part of this problem. The magnetic flux linked through the second point. And that is as a function of time. Here it can be represented as a function of time. Five to t is equal. No. In the second part of the problem, we have to find the maximum MF induced in this second coil. So using, um if induced is equal to if we use only the magnet you it will be given by the time rate of change of flux through the second coil. Or we can say time derivative of the flux, or we can say differentiation of the flux. So it is given us the constant new not into anyone into end to party are square. I am here. This is my note and one and two I Empire square by l and the differentiation of sign is cause omega T and into omega. So this MF induced in the second solid annoyed as a function of time comes out to be immune not into priority square into anyone into end to I am Omega, divided by l into course Omega T But we have to find the maximum of India's. So maximum MF induced means this complete you. So this is new not bye arty square and one and two I am Oh, my God! Divided by length of the solenoid And here it becomes an answer for the second part of this problem. Thank you.

Hi in the given problem there are too sorry noise and for these two solenoid it is given that the areas of cross section are the same. So we can let it be only. Their lands are also same. Elvin is equal to L. To let it be L only. But as far as their number of transport unit length are concerned. If and two means a number of times per unit length in the second solenoid is and then and one means those in the first solenoid are the wise off. And so using the expression for self induct ins L. Is equal to um unit and I your L one will be given by mu note and one into I and two will be given by new not and two into I therefore L two by L. one will become equal to new note and I divided by mu not and when I cancelling all other things, this is anti by anyone. Now for an end to this is and for anyone this is twice often cancelling this. Also we get health to is to Elvin is equal to one is 2, two. So here we can say option B is correct. Thank you.

Okay, let's put the question to co axial solenoid. Are there that is having different radio. Okay, so this is one solenoid and this is the and this radical er is the other solenoid. Okay, so access is same for both of these. Okay, this is the smaller diesel Leonard and this is the big radiation and right, okay. And the wire are like this. Okay, and this is like this, understand? So what is happening here? Okay. As for the question uh it is assumed that fun is the magnetic force on the inner solar energy due to the ultra one. Okay. F one. Okay. Force on inner on in urban due to Due to the outer one. Okay, Outer sole annoyed. And F. Two that is assumed. Okay, that is a magnetic force on outer sole annoyed on outer solenoid due to in a solid night. Okay, so these two solenoid are co axial. So let's take a uh right view. Okay from here. So this is the so you know that is outer and this is the inner Okay, and this is the center of both of these. That is same. Okay. And what is happening here? We know that the magnetic field uh inside the solitary that is given by BC was too mu not and I okay, you know it is a constant and is the number of loop. Okay. And i is the current flying in this current is playing in the same direction? Okay, here it is same here, it is same direction. So inside this one and two this inside this one numbers all annoyed. There will be magnetic will be but we know that outside the magnet outside the solar night there will be zero magnetic field. Okay this is inside and this is outside so there will be no magnetic field due to The Solenoid one. Outside the outside the this solenoid. Okay so we can say there is uh no magnetic uh magnetic field due to the inner soul, annoyed in the outside region will be zero. Okay here it is zero. So magnetic force on outer sole annoyed due to inner soul annoyed that is given the caution, F two will be zero. Understand you understand that point. That magnetic field due to inner soul annoyed in the outer region this region. Okay this reason is zero. So the magnetic force on the outer solar and I do too in urban will be also zero. So I have two is zero. It means on the outer there will be no force. Okay, it means there will be no force and we know that new to start low, every action has an equal and opposite reaction. Okay so if there if this have two is zero then F one surely will be zero. Okay because if there is some value of F one. Okay, F two will be surely there. Okay if F two is their F one should be zero. Otherwise there will not be in a stable condition is there? Okay so F one should also zero due to have 20. This F one should also be zero. Understand the point. So the answer will be F one that is close to have to and that is equal to zero. Okay, F one that is equal to have to, that is equal to zero. That is given an option D. So option D will be our final answer of discussion. Thank you.

So first we need to calculate the mutual in doctors meet reluctance. M is the same football coils so we can write it as follows. A number of turns and quality multiplied by the flux in used in coil a bike oil B five b A divided by the current flowing through coil eight and we have these values. So the number of tons of oil be is 700 and the flux Lukoil A Each turning quite eight is 90 micro embers on 90 times 10 to the minus six rivers all over. The current is flowing in quite a which is 3.5 MPs. You can see we suppress the units here and so we get a mutual inducted its 18 Really, Henry. Now we wish to calculate herself in doctors on eight. So the self indulgence of a it's simply a member off tons in a multiplied by the magnetic flux through a all over the world by the current anything and so again, these numbers I know it so quite a has 400 tons and I mean it. Influx to eight is the 100 times 10 to the minus six rivers. Oh my. We can't going to lay off 3.5 and piers and again if you do the calculation, get the self conductors of eight to be 34.3. Milly Henry's and finally, Southie induced EMF and be is equal to minus M mutual inductions. Multiply by the I Hey DT, The rate of change of current in a gives us I'm induced, emits and quite be. And again these values are known. So that's minus a team. 1,000,000 reasons you calculate for the future Inductions on the current is changing. Irit 0.5 m piers a second. Hence we get PMS inducing coil be off a minus nine Milly wars.


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