Problem

Construct Your Own Problem Consider a mass separa…

04:21

Problem 89 Hard Difficulty

Unreasonable Results A surveyor 100 $\mathrm{m}$ from a long straight 200 $\mathrm{-kV}$ DC power line suspects that its magnetic field may equal that of the Earth and affect compass readings. (a) Calculate the current in the wire needed to create a $5.00 \times 10^{-5} \mathrm{T}$ field at this distance. (b) What is unreasonable about this result? (c) Which assumption or premise is responsible?

Answer

Part $(a) : 25 \mathrm{kA}$
Part $(\mathrm{b}) :$ The current found in part $(\mathrm{a})$ is so large.
Part $(\mathrm{c}) :$ The $100-\mathrm{m}$ distance is unreasonably long.

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Physics 102 Electricity and Magnetism

College Physics for AP® Courses

Chapter 22

Magnetism

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Video Transcript

we need to know if it is reasonable to consider and why you're in your household. Reach creates additional magnetic field. Why were way we're measuring the direction we're using. Got compass. So how long this works is right? Uh, Dairy's just and my just a magnetic field created by the airs, then Columbus. It's just a mind it and it would align it's area. Would l spare airline along the air magnetic field. And we know that a ares magnetic field is coming from one hole and is going to end Interpol. Ah, So did waiting to aero showthe direction off the north or south. And if obviously there is external magnetic field other than I didn't hear the magnetic field, the reading would be inaccurate because the magnetic field, uh, it has changed. It doesn't show the direction off north are south Isa. We chose some other direction. And ah, in this case, if we're standing, we're sending 100 meters from why you're which is carrying a normal, normal current, and we need a tow. Find out what current is necessary to create. Ah, the air's magnetic field, huh? Tow this distance. So Earth's magnetic field these fine 10 lines. It's fry Bassler, and we're standing 100 meters apart from this wire. Ah, that's a r. And what is the current? So we know that know how to find a magnetic field created by a long straight wire which is being who's and the migrant constant to me or not be over too, right? And from here e to I are being over me, you know? And what is You know, it is humanity constant, which is 1.26 10 minus seeks, and it's unique. Oh, cheers, I if I, uh I'm minus two second minus two. Just not double turkey. It's going. It should be correct. Yeah, uh, this is mu. And from here, the current should be two complaint 48 10 minus 10 in the fourth power. I'm her Ritchie's owned 25 kilo on hers. And of course, if we look this current in normal normal household wire, this is a huge cure current. Usually the current is like several encores. Uh, you in a normal situation. Uh, so decent, reasonable toe concho that on the normal current would create uh, the magnetic field which would have effect beach with FAA. The reading off a compass. And what is unreasonable in this assumption is that thes distance 100 meters is, uh too are too large. Eso at this distance, they would want to be any effect created by by wire, which is carrying you. They say normal current. So we should We shouldn't worry if we air a distance, but we should worry if we are closer. Tow this wire, Let's say maybe one meter a part of something like this, huh? The effort could be meaningful back in these assumptions. Uh, we shouldn't worry about the effect created by a normal current at this distance.

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