OBJECTIVE:  

1) I will be able to apply the "right hand rule" to calculating magnetic forces after today's class

2) I will be able to apply the "right hand rule" to calculating magnetic forces after today's class

WORDS/FORMULAE FOR TODAY

TERMS

• Magnetic Field (B): A vector value (I dunno why "B")
• 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)

WORK O' THE DAY: 

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Today we begin our investigations into magnetic fields.

Consider the case of the planet Mars. Mars is, in most every sense of the word a dead planet. Some billions of years ago Mars' developed an astounding series of volcanoes (including Olympus Mons-- shown below

Because Mars' core is smaller and cooler than the Earth's (more about that in a moment) a sustainable tectonic system was impossible and volcanism ceased. Without a steady resupply of CO₂ and other gasses to replenish the atmosphere through volcanism, Mars eventually lost 98% of its atmosphere to space.

Just in case that wasn't bad enough for any life struggling and/or prospering during those times, the lack of a dynamic core also led to the loss of....

 

WHAT?

 

 

MAGNETIC FIELD... It may interest you to know that the Earth's outter core is essentially a massive amount of ionized metal moving in a circular motion... which means MAGNETIC FIELD!!!

.... which left the Martian surface *totally* exposed to cosmic rays and other high energy ionizing radiation from space.

Although it is difficult to see here, magnetic fields lines DIFFER from electric field lines in that they do NOT stop at the surface-- they continue through the object (in this case the Earth) to form a loop.

Keep that in mind

The reason why magnetic force is *always* perpindicular to magnetic field lines has to do with Lorentz Contractions and special relativity... if you're curious along those lines, check this out

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Magnetic Force:

A charged particle in a magnetic field experiences a force perpendicular to the magnetic field.

• That force is determined by:
  • the charge (q) on the particle
  • the velocity of the particle
  • the magnitude of the magnetic field

Mathematically we represent those quantities thusly:

F_B = qv x B

This is the 'cross product' which we use to find vector quantities (ACK!)

Or

We can find the MAGNITUDE of the magnetic force:

F_B = qvBsinθ

Note: since we're after the magnitude of the force here, we don't really care if 'q' is positive or negative so we use the absolute value of q

• Clearly when the motion of the charge is in the direction of or directly against the direction of the magnetic field the magnetic force is is at a min (zero).
• Likewise when the motion of the charge is perpendicular of the direction of the magnetic field the magnetic force is at a max.

It can be a bit tough to keep track of which of the three is moving where... so we use what we call the "Right Hand Rule" to do that

(HINT: Think FDF (Force/Direction/Field)

I LIKE THIS ONE

Or This One: ("Current" is the same direction as velocity)

NOT SO MUCH

Magnetic fields are measured in units of force, charge and velocity (as you might expect)

As you also might expect, we'll give it a name of another physics pioneer, in this case Nicola Tesla (like the car, and yes that's why)

1 T = 1 N/(C)(m/s)

Let's try some practice right-hand-ruling (remember: Force/Direction/Field) Hint: try point in the direction of motion FIRST

B = Magnetic Field

F_B = Magnetic Force

Find the direction of the magnetic force below

F_B= Up (+y direction)

Find the direction of the magnetic force below

This one is tricky... the convention is for a POSITIVE test charge (as per previous... try again)

Find the value using a positive charge and reverse it!

(out of the page)

Find the direction of the magnetic force below

ACK! What's wrong here?

Hint: Think sin

Find the direction of the magnetic force below

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Take a look at example 29.1 (use the right hand rule) to show the direction of the electron's motion, the direction of the magnetic field acting on that electron and the magnetic field of the TV

 

Notes on convention:

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Fun with cross products -- using the right hand rule with cross products

Let's try one together:

(i + 2j + 3k) x (-2i + j - 2k)

We have *several* options as to how to continue. If we go wayyyyyy back to chapter 11 and take a gander at the formulae on page 336:

1) The 'standard' route using a matrix as per 11.8 (boring)

2) Read 'em and weep method using 11.7a-d (rote memorization)

3) DIY using right hand rule (YES!... but maybe not best to do all the time)

1) write out the equations for (i + 2j + 3k) x (-2i + j - 2k) and now build a matrix of all possible permuations:

i x -2i	i x j	i x -2k
2j x -2i	2j x j	2j x -2k
3k x -2i	3k x j	3k x -2k

If you're good in 3d imagery get to it.... if you're not so hot at modeling 3d in your head, sketch a simple xy plane and use your pencil to show z out of the page or into the page.

Let's divide and conquer this between your groupies please

"Crossing" in the same direction is easiest, let's knock them out:

i x -2i = 0	i x j	i x -2k
2j x -2i	2j x j =0	2j x -2k
3k x -2i	3k x j	3k x -2k =0

Now time to practice right-hand-ruling:

	i x j = k	i x -2k = 2j
2j x -2i = 4k		2j x -2k = -4i
3k x -2i = -6j	3k x j = -3i

so

-4i - 3i + 2j - 6j + k + 4k

combining like terms

-7i -4j + 5k

Check with vector calculator

 

HOMEWORK: