Magnetism 10 - Gauss's Law (Magnetism Flavor)

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M/c O' the Day:

Today's Safari Guide is:

Ian!

Released Exam Problem

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OPENING QUESTION:

Consider the following B field:

The direction of the B field is?

If we roll a penny through that B field from right to left how will it be deflected? Why?

If we add an electron cruising in from the left side it will be deflected... how? Why?

If we add a proton cruising in from the right side it will be deflected... how? Why?

A gravitational field is an interesting concept, but in order for an actual gravitational FORCE to be present, there must be _________________?

A electrical field is an interesting concept, but in order for an actual electric FORCE to be present, there must be _________________?

A magnetic field is an interesting concept, but in order for an actual magnetic FORCE to be present, there must be _________________?

Did you say charged particle??? Then your answer was incomplete. Write down the two basic formulae that allow us to calculate magnetic force... There is a roadmap there, what are they saying MUST be true in order for a magnetic force to exist?

Consider the following wire:

What is the B field above the wire? What is the B field below the wire?

If we dropped a penny above the wire? What direction would it be deflected?

If we dropped a proton from above the wire what direction would it be deflected?

If we dropped an electron above the wire what direction would it be deflected?

 

We gotta nice long straight wire with constant current... right away that VERITIBABLY SCREAMS... what?

What is the result of that calculation?

What if there are loops?

 

 

 

OBJECTIVES:  

I will be able to derive an expression relating B field strength to the number of coils in a solenoid during today's class.

I will be able to use Gauss's Law in Magnetism to <> during today's class

WORDS/FORMULAE FOR TODAY

TERMS

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

CONSTANTS:

 

UNITS:

      • Tesla = T defined as 1 N/C(m/s)

FORMULAE:

      • ∮B ∙ ds = μoI: Ampere's Law
      • FB = qv x B
      • FB = qvB
      • FB = qvBsinθ
      • FB = IL x B
      • FB = ∫I ds x B NOTE: AP Version is: FB = ∫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 = (μoI/4π)(dℓ x r̂ )/r2 (BS Law)
      • B∮ds = μoI (Ampere's Law)
      • B = μo(N/ℓ)I=μonI
      • Φ =∫B ∙ dA = BAcosθ

WORK O' THE DAY: 

Gauss revisited:

ΦB =∫B ∙ dA = BAcosθ

What do you suppose Φ is in this context? Please converse with your crew...

Also, what is the significance of the *dot* product here?

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Here be Ampere's Law:

B∮ds = μoI

What is the significance of the ∮integral?

How have we used that so far?

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Answers:

The ∮integral requires use to move around an enclosed area. Up until now we've been talking about a long straight wire.

What better shape to use to enclose such a beastie than a ring of radius "r"... that works very, very nicely.

But... what if the area we were interested in enclosing was a rectangle(???), would that still work?

Let's try:

Consider the following sitchation--

A long straight wire is shown some distance away from a rectangular loop of wire as shown:

Work with your group to come up with a strategy as indicated...

Annotate your steps

DO NOT PEEK until you have a strategy to begin, then *carefully* peek if you need additional hints...

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COURSEWORK: 30.47 & 30.48 begining on page 930

 

 

ANSWERS:

 

 

 

 
STUDY GUIDE: