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: Starting with Ampere's Law, please derive an equation that shows the B field at some distance away from a solenoid with n coils.

 

 

 

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 d 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)(d 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: