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Biot-Savart Law

Hello,

I have been reading a book to see how the magnetic field due to a straight conductor is derived using Biot-Savart law. I have a little question from the attached (pdf) page. It looks from figure 30.3 that the angle theta is positive, so how can we take tan⁡θ=a/(−x)\tan \theta = a/(-x) (highlighted text), irrespective of the fact that we have dx in the negative x-axis? Taking negative sign with x would give a negative value of theta, which seems quite wrong. I'm sort of confused. A little explanation would help.

Many thanks.
Physics for Scientists and Engineers, 6th Edition 929.pdf111.6KB
It's tan theta that is negative, not theta.
Because the tan of an angle is negative, that does not imply that the angle is negative.
Angles can be in different quadrants, giving positive or negative values of sin, cosine and tangent. The angle itself is positive.
For example, sin 90 = +1, sin 270 = -1
270 is not negative, is it? It's just in a different quadrant.
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Avatar for SalBhatti
SalBhatti
OP
13
Original post by Stonebridge
It's tan theta that is negative, not theta.
Because the tan of an angle is negative, that does not imply that the angle is negative.
Angles can be in different quadrants, giving positive or negative values of sin, cosine and tangent. The angle itself is positive.
For example, sin 90 = +1, sin 270 = -1
270 is not negative, is it? It's just in a different quadrant.


Oops.:facepalm: Many thanks. :smile: Btw could you recommend me a good University Physics Book?
Original post by Zishi
Oops.:facepalm: Many thanks. :smile: Btw could you recommend me a good University Physics Book?


I think this question has been asked recently here.
Does a search bring it up?
Reply 4
Avatar for SalBhatti
SalBhatti
OP
13
Original post by Stonebridge
I think this question has been asked recently here.
Does a search bring it up?


Nope, the search brings up A Level books or books on specific topics (quantum mechanics) only.
Original post by Zishi
Nope, the search brings up A Level books or books on specific topics (quantum mechanics) only.


It's probably better to ask this in a new thread here.
I think you will get a better reply from other undergrads.
State whether you are asking for a general university physics text or a specific area such as mechanics.

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