OBJECTIVE:  I will be able to make basic calculatations regarding magnetic fields during today's class (AND develop a working understanding of the solar wind too!)

 

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:

• F_B = qv x B (vector value)
• F_B = qvBsinθ (F_B magnitude of only)

FRQ'S

WORK O' THE DAY: 

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CLOSE YOUR BOOKS, CLOSE YOUR NOTES... .

Have something to write with and write on please!

 

Our FIRST m/c presentation: Mr Yi!

Oh and by the by, with most *profound* apologies to Mr Yi, please do use the template for the your basic plan, but do a HAND WRITTEN (heavily and accurately and humoursly(?) annotated) solution.

It turns out the equation editor on google docs is awfully difficult for me to translate onto my page... Irvin did a LOT of work with the equation editor, and I apologize and most humbly and publicly seek his pardon...

• Generally -- introduce your m/c problem
• Give your students about 1 minute to identify the problem, then give them another minute (or 2) to collaborate on solving.
• Then take another minute (or 2) to show your solution.

 

QUESTION for you to ponder... the units of measure for magnetic field are the Tesla (T). Why do you suppose we rarely (never?) actually break those down into smaller units?

 

Answer:

Consider our pivotal equation for magnetic force:

F_B = qv x B

or more generally:

F_B = qvB

Rearranging for B:

F_B/qv = B

and expressing in units only:

N/[C(m/s)]

Uh umm.... ok? Let's stick with T

Let's revisit the idea of magnetic fields... specifically magnetic field lines. Recall from yesterday that the Earth as magentic field lines extending out from the north magnetic pole and returning at the south magnetic pole.

The solar wind is a massive, constantly changing, yet continuous blast of charged particles flowing out from the sun.

(and ONLY charged particles) interact with magnetic field lines emanating from the Earth's poles.

That means that even if the sun has a massive weather event (in other words it emits a much higher number of charged particles in the solar wind than usual, but yes, we do call that the solar weather) the magnetic field intercepts those particles and exerts a force upon them.

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Quick Time Out -- Recall that magnetic force is qv x B which we can (and do) shortcut to:

F_b = qvb

Keep in mind that the particle is VERY DEFINITELY NOT moving in the direction of the magnetic force when it starts to tangle with Earth's magnetic field.

Students often form a misconception that the particle is being pushed by the magnetic force (which seems reasonable... unfortunately, it ain't accurate!). The particle is definitely affected by that force as we shall see.

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Because of the nature of their motion through space relative to the magnetic field lines, the charges experience an unbalanced force in the plane perpendicular to the field lines.

Since there is no force in the direction of motion of the particle, it ends up making a spiraling motion around the axis of the field lines!!

As that particle spirals closer and closer to the Earth along those field lines it almost certainly will collide with an electron in an oxygen or nitrogen atom in the upper Earth's atmosphere.

That collision results in the electron jumping to a higher energy state (or, somewhat more rarely, getting blasted away from the atom entirely). That electron drops down to a lower energy state and... VOILA:

 

 

aurora australis or aurora borealis!

Quick Aside On CME's.... read HERE if you're interested

Keep your books closed (please) but please do open your notes and...

Picture an α particle, blasting along in the solar wind heading towards the earth when... *wham* it gets snared by one of Earth's powerful magnetic field lines!

Work with your group to determine an expression that relates the magnetic force to the circular (hint! hint!) motion of that particle.

Now please work with your group to *derive* an expression for the period for such a particle as it spirals around a magnetic field line.

(hint: think of things like f and ω and π oh my!)

GO!

 

Now please do a bit of research and find values for your variables and solve....

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Now with that same idea in mind, calculate the magnetic field produced by the Large Hadron Collider (located along the French/Swiss border area) when it pumps up electrons to the 7 TEV (tera electron volts) range.

Hint: 1 electron volt = the energy level achieved by an electron when it is exposed to an electric potential of 1 volt (or 1.6 x 10^-19 joules)

 

Now just for fun, imagine we have a charged particle the size of a baseball (mass = .45 kg)... how fast would the LHC get that thing going?

 

COURSEWORK:

Work through example 29.2 following our usual steps

Take a look at example 29.3 ( don't forget ∆U = q∆V)

Problems: 29.13, 29.14