NCEES Practice Exam problem 516

I'm stumped on this one, and I don't have any good Electromagnetic books. Any tips? I would post the question, but it would make no sense without the diagram.

I don't understand with the path for leg B is "d", and leg C is "3d". To me, it seems like B should be "3d", and C should be "5d".

SteveR said:

To me, it seems like B should be "3d", and C should be "5d".

Click to expand...

All of the flux generated by the coil has to pass through the first and last segments of length "d". It splits to go through legs B and C. The problem is to determine how much goes through each leg. The math works the same as for current division. Leg C has three times as much "resistance" as leg B. It will then carry 1/4 of the total flux.

Does this help?

Jim

I've read through your explanation a few times, but still can't quite get it, which is driving me crazy since this doesn't seem like that complicated of a problem. I still can't manage to get Leg C having 3x the resistance of B, or 3x the path distance. For the B path, I'm counting 1 horiz. d + 1 vert. d + 1 horiz. d to get back to the coil, which is 3d. For the C path, I'm counting 2 horiz. d + 1 vert. d + 2 horiz. d = 5d. That gives me a ratio of 5:3, which is nowhere close to 3:1. Thanks for your help!

IFR_Pilot said:

All of the flux generated by the coil has to pass through the first and last segments of length "d". It splits to go through legs B and C. The problem is to determine how much goes through each leg. The math works the same as for current division. Leg C has three times as much "resistance" as leg B. It will then carry 1/4 of the total flux.
Does this help?

Jim

Click to expand...

grownupsara said:

I've read through your explanation a few times, but still can't quite get it, which is driving me crazy since this doesn't seem like that complicated of a problem. I still can't manage to get Leg C having 3x the resistance of B, or 3x the path distance. For the B path, I'm counting 1 horiz. d + 1 vert. d + 1 horiz. d to get back to the coil, which is 3d. For the C path, I'm counting 2 horiz. d + 1 vert. d + 2 horiz. d = 5d. That gives me a ratio of 5:3, which is nowhere close to 3:1. Thanks for your help!

Click to expand...

I think the only thing you are missing is that ALL of the flux travels through the first and last segments. Try re-drawing the problem as an electrical circuit with a 3mA DC source where the coil is and 1-ohm resistors where each of the legs.

Let me know if this helps.

Jim

Edit: Changed source to a 3mA current source.

Hey, that finally made it click! I scanned in the work I did using your advice, with each d segment = 1ohm resistance. Thanks!

Thanks guys,

I finally got this one!

arty-smiley-048:

Could you please explain it electrically ? I saw your posts of replacing each leg with 1 Ohm and using 3mA as current source.

Still cant figure it out :-/

Nik

IFR_Pilot said:

SteveR said:

To me, it seems like B should be "3d", and C should be "5d".

Click to expand...

All of the flux generated by the coil has to pass through the first and last segments of length "d". It splits to go through legs B and C. The problem is to determine how much goes through each leg. The math works the same as for current division. Leg C has three times as much "resistance" as leg B. It will then carry 1/4 of the total flux.

Does this help?

Jim

Click to expand...

How's this:

IFR_Pilot said:

I think the only thing you are missing is that ALL of the flux travels through the first and last segments.

Click to expand...

Doesn't 3/4 of the flux travel thru the middle segment?

BamaBino said:

IFR_Pilot said:

I think the only thing you are missing is that ALL of the flux travels through the first and last segments.

Click to expand...

Doesn't 3/4 of the flux travel thru the middle segment?

Click to expand...

Using current division, the current/flex divides as inverse of path resistance, therefore, 1/4 of the 3mA = 0.75mA through outside segment which leaves 3/4 * 3mA = 9/4 = 2.25mA through middle segment. They'd better add to 3mA.