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 (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 (Ampere's Law)
• B = μ_o(N/ℓ)I=μ_onI
• Φ =∫B ∙ dA = BAcosθ

WORK O' THE DAY: 

Gauss revisited:

Φ_B =∫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 = μ_oI

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

 

 

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