Magnetism 10 - Gauss's Law (Magnetism Flavor)


M/c O' the Day:

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Released Exam Problem


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.





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



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




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


      • 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


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?


Here be Ampere's Law:

B∮ds = μoI

What is the significance of the integral?

How have we used that so far?




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...


COURSEWORK: 30.47 & 30.48 begining on page 930