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## Main Question or Discussion Point

A friend of my has trouble understanding these two questions. I tried to explaining it to her but my explaining skill kind of sucks so I am wondering if someone can explain these questions better.

First question is this.

4- A very long solenoid with a circular cross section and radius r1= 2.80 centimeters with ns= 280 turns/cm lies inside a short coil of radius r2= 3.40 centimeters and Nc= 26 turns.

http://capa.mcgill.ca/res/mcgill/dcmcgill/oldproblems/msuphysislib/Graphics/Gtype66/prob05a_coils.gif

If the current in the solenoid is ramped at a constant rate from zero to Is= 1.70 Amperes over a time interval of 64.0 milliseconds, what is the magnitude of the emf in the outer coil while the current in the solenoid is changing?

She was wondering why we use the radius/area of the solenoid in calculating the change in magnetic flux rather than say the area of the big coil. She thought that the magnetic field lines from the solenoid would spread out and affect the big coil.

Here is her original question "why don't we use the second radius...the one of the outer coil. I know inside the solenoid the magnetic field is constant, but won't the outer coil feel a smaller magnetic field, and therefore flux, because it is at a certain distance from the inner solenoid? Or does flux only have to do with the change, and the change will be proportionally the same, no matter the distance?"

The way I said is that.. Magnetic field lines inside a solenoid is like this..

http://p3t3rl1.googlepages.com/pquestion1.jpg

So when you put the solenoid inside the big coil (side cross sectional view), it only affects the area that belongs to the solenoid and no where else..

http://p3t3rl1.googlepages.com/pquestion2.jpg

She thought the magnetic field lines would go off like these and affect the big coil....

http://p3t3rl1.googlepages.com/pquestion3.jpg

Well my explanations didn't really work as she is still confused about it.

Can anyone reword what I said so that she can understand it?

Also, she is wondering why we can't use the mutual inductance equation to solve it..

The equation is.. [tex] E= -L\frac{\Delta I}{\Delta t} [/tex]

If you can find L, then it should work right?

Again, here is her original question.."Apart from the fact that you need the length of the solenoid to calculate the inductance using that method, why, conceptually, can you not do it that way?"

I have no clue. Can anyone explain why conceptually it is a wrong method?

Ok, the second queston is something like this..

The magnetic field B at the center of a circular coil of wire carrying current I is

[tex] B=\frac{\mu NI}{2r} [/tex]

The question asks.. If you use a greater number of turns and this same power supply (120 V), will a greater magnetic field strength result?

In class the prof explained B ~ NI. R ~ N ( more length of wire, higher resistance) therefore I ~ 1/N. Thus, the increase in B field strength caused by greater N turns would be canceled by the reduced current exactly so that the magnetic field stays constant. The thing is though, [tex] R = \rho\frac{L}{A} [/tex]. Different wires have different resitivity, so wouldn't some wire experience less of a decrease a current when more turns are wrapped around, so that the net affect is increase in B field?

Thanks and have a good day!

First question is this.

4- A very long solenoid with a circular cross section and radius r1= 2.80 centimeters with ns= 280 turns/cm lies inside a short coil of radius r2= 3.40 centimeters and Nc= 26 turns.

http://capa.mcgill.ca/res/mcgill/dcmcgill/oldproblems/msuphysislib/Graphics/Gtype66/prob05a_coils.gif

If the current in the solenoid is ramped at a constant rate from zero to Is= 1.70 Amperes over a time interval of 64.0 milliseconds, what is the magnitude of the emf in the outer coil while the current in the solenoid is changing?

She was wondering why we use the radius/area of the solenoid in calculating the change in magnetic flux rather than say the area of the big coil. She thought that the magnetic field lines from the solenoid would spread out and affect the big coil.

Here is her original question "why don't we use the second radius...the one of the outer coil. I know inside the solenoid the magnetic field is constant, but won't the outer coil feel a smaller magnetic field, and therefore flux, because it is at a certain distance from the inner solenoid? Or does flux only have to do with the change, and the change will be proportionally the same, no matter the distance?"

The way I said is that.. Magnetic field lines inside a solenoid is like this..

http://p3t3rl1.googlepages.com/pquestion1.jpg

So when you put the solenoid inside the big coil (side cross sectional view), it only affects the area that belongs to the solenoid and no where else..

http://p3t3rl1.googlepages.com/pquestion2.jpg

She thought the magnetic field lines would go off like these and affect the big coil....

http://p3t3rl1.googlepages.com/pquestion3.jpg

Well my explanations didn't really work as she is still confused about it.

Can anyone reword what I said so that she can understand it?

Also, she is wondering why we can't use the mutual inductance equation to solve it..

The equation is.. [tex] E= -L\frac{\Delta I}{\Delta t} [/tex]

If you can find L, then it should work right?

Again, here is her original question.."Apart from the fact that you need the length of the solenoid to calculate the inductance using that method, why, conceptually, can you not do it that way?"

I have no clue. Can anyone explain why conceptually it is a wrong method?

Ok, the second queston is something like this..

The magnetic field B at the center of a circular coil of wire carrying current I is

[tex] B=\frac{\mu NI}{2r} [/tex]

The question asks.. If you use a greater number of turns and this same power supply (120 V), will a greater magnetic field strength result?

In class the prof explained B ~ NI. R ~ N ( more length of wire, higher resistance) therefore I ~ 1/N. Thus, the increase in B field strength caused by greater N turns would be canceled by the reduced current exactly so that the magnetic field stays constant. The thing is though, [tex] R = \rho\frac{L}{A} [/tex]. Different wires have different resitivity, so wouldn't some wire experience less of a decrease a current when more turns are wrapped around, so that the net affect is increase in B field?

Thanks and have a good day!

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