(b) Inside the solenoid, what is the magnetic energy density...

(b) Inside the solenoid, what is the magnetic energy density (J/m^3) far from the ends of the solenoid? 15.147 J/m^3 the tolerance is +/-5% Part 3 (c) What is the total magnetic energy, in the approximation that there is little magnetic field outside the solenoid and the magnetic field is nearly uniform inside the solenoid? the tolerance is +/-5%

Transcript

0:00 Hello sturon.

00:01 So our question is inside the solenoid, what is the magnetic energy density? which we have to find out in zool per meter cube, far from the ends of the solenoid.

00:13 So let's solve this.

00:14 We have to find out the magnetic energy density.

00:17 So number of turns, we are writing here the quantities which is given to us.

00:22 First is number of terms.

00:26 N is equals 200 given to us.

00:30 And the radius the radius r is 1 .8 cm that is when we convert in a meter this will be 1 .8 multiply by 10 to the power minus 2 and its meter okay and length of solenoid it's also given to us a length of which is 26 cm 26 multiplied by 10 to the power minus 2 meter okay and current through solenite current solenoid so it is given i is equal to 6 a okay 6 ampere this 6 ampere 6 a that means 6 ampere okay and part a we have to find out the magnetic energy density so first we must know that magnetic field inside the solenoidal is b is equal to mu not capital n i divided by n and clearly you can see that these values are given to all.

01:39 Okay and now if i have to find out the magnetic energy density, magnetic energy density.

01:51 So formula for this, mu b is equals to u b is equal to b square this is square of magnetic field, magnitude of magnetic field and divided by 2 muon.

02:04 Now if you will put the value of b here, so this will be u b is equal to m u b is equal to m u .n square n square i squared and divided by l square to mu not and mu not will be cancelled out so this will be ub is equal to mu not n square i squared divided by 2 l square so easily we can put the values in it because we know the value of mu not and i l all things so ub is equal to the value of muonotus 4 pi multiply by 10 to the power minus 7 the value of n is 100 so square of the value of n is given to us is 1 ,000 square and the value of i is current is 6 n squared and divided by 2 multiply by the value of l is 0 .26 which is given to us in question so it is square so when we solve all this term this will be 334 .6075.

03:16 6075.

03:16 This is in jule meter cube...

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