OBJECTIVES:  I will be able to explain Ampere's Law and do basic problems related to it during today's class.

WORDS/FORMULAE FOR TODAY

TERMS

• Magnetic Field (B): A vector value
• Magnetic Force (F_B): Also a vector

CONSTANTS:

 

UNITS:

• Tesla = T defined as 1 N/C(m/s)

FORMULAE:

• ∮B ∙ ds = μ_oI: Ampere's Law
• F_B = qv x B
• F_B = qvB
• F_B = qvBsinθ
• F_B = IL x B
• F_B = ∫I ds x B NOTE: AP Version is: F_B = ∫I dℓ x B
• v = E/B
• τ = IAB (torque in a current carrying loop)
• τ = NIA x B (torque in a current carrying loop - vector version)
• τ = μ x B (torque in a current carrying loop - abbreviated version)
• KE = q₂B₂R₂/2m
• dB = (μ_oI/4π)(dℓ x r̂ )/r² (BS Law)
• B∮ds = μ_oI

WORK O' THE DAY: 

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M/c O' the Day:

Today's Safari Guide is:

AARON!

Released Exam

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ACK! Looks like I got a tad too clever with my solution to 30.3 yesterday.... I only looked at the the *finalize* part of the author's solution, which to me at least, seemed like where the final answer should be..... blechhh. It turns out the "finalize" section shows the B field at the center of the loop, which is what I inadvertantly ended up doing <sigh>.

Like I said, this Biot Savart ain't easy.

Anyhow, my solution did not solve for the B field at point P (some distance away from the loop) but actually at the center of the loop...

The silve lining is that that solution is very much germain to our work today...

So let's mush on....

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As you might suspect the magnetic field surrounding a current carrying wire is curved.

If we measured the direction of the mag field at various places we would see:

Provided of course the current was sufficiently strong (remember, the Earth's magnetic field is present too!)

Let's take a look at

B ∙ ds

(notice ds is a vector related to the circular path of the magnetic field, NOT the current as in the B-S law).

Also notice we are looking at a "dot" product here... so the rigors of right-hand-ruling are not quite as severe here (we still use rhr to find which direction to integrate and such)

We found at the VERY end of yesterday's work that there is an interesting relationship between the magnetic field and a current carrying loop:

B = μ_oI/2πr

Much to our rescue after the rigors of BS, we now have a much simpler way to deal with finding the B field at some distance r from a current carrying wire IF:

• The B field is constant
• A HIGH degree of symetry is present in the wire
• We enclose the wire in a nice symetric imaginary shell and then integrate around that shell (sound familiar?)

Mesdames et Messieurs et Mes Amis:

I give you... <drum roll please>

Ampere's Law

B∮ds = μ_oI

which is a WHOOOLE lot easier to work with than the B-S Law

Ampere's Law is a SIMPLIFIED version of one of Maxwell's Equations (there are four of 'em) that have successfully ruled over, guided and frustrated students over 150 years!

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Ampere's Law is similar to Gauss' Law in that we'll really only use it with highly symetrical situations and can be loosely stated as:

We can find the magnetic field at a uniform distance around a current carrying wire by:

B∮ds = μ_oI

Which pretty much always go to:

B2πr = μ_oI

WAIT FOR IT, WAIT FOR IT, WAIT FOR IT!!!!

B= μ_oI/2πr

ALSO, please note that as in Gauss' Law, we can draw an "amperian" surface inside which to analyze our magnetic fields.

Take a look at just the FIRST PART of 30.5...

Now please do this:

1) Derive Ampere's Law from the work we did on example 30.3 yesterday (you are free to use online resources)

2) Rewrite that *nasty* example 30.1 in such a way that we CAN use Ampere's Law to solve it and not be REQUIRED to use BS.

3) Write an approximate 10 minute lesson plan to teach your students about Ampere's Law by comparing it to Gauss' Law (and whatever else you think is appropriate. You may use online resources for this).

4) Be prepared to give your lesson first thing tomorrow

GO!

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HOMEWORK: