Curly Electric Fields

  • #1

Homework Statement



23-068-E_inside_and_outside_magnet.jpg


The magnetic field is uniform and out of the page inside a circle of radius R, and is essentially zero outside the circular region (see the figure). The magnitude of the magnetic field is changing with time; as a function of time the magnitude of the magnetic field is (B0 + bt^3). r1 = 6.4 cm, r2 = 63 cm, B0 = 1.5 T, b = 1.4 T/s3, t = 0.8 s, and R = 15 cm.


(a) What is the direction of the "curly" electric field at location P, a distance r1 to the left of the center (r1 < R)?

(b) What is the magnitude of the electric field at location P? (Hint: remember that "emf" is the integral of the non-Coulomb electric field around a closed path.)

(c) What is the direction of the "curly" electric field at location Q, a distance r2 to the right of the center (r2 > R)?

(d) What is magnitude of the "curly" electric field at location Q?


Homework Equations



E∫dA = emf
emf=dΦB/dT
ΦB = BxA


The Attempt at a Solution



I have no clue. It says to use the E∫dA = emf, but emf is not given. That (B0+bt^3) is just confusing me.
 

Answers and Replies

  • #2
kuruman
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Faraday's Law says emf = -dΦ/dt. Does that help?
 
  • #3
Not much because I don't know what to do with it. What would the flux be? Would it be
emf = -dΦ/dt

Φ = BxA

emf = (-d/dt)BxA?

Does B = B0 + bt^3?
 
  • #4
kuruman
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Not much because I don't know what to do with it.
Then you need to read your textbook and learn about Faraday's Law.
What would the flux be? Would it be
emf = -dΦ/dt

Φ = BxA

emf = (-d/dt)BxA?
I would not put a cross in between because it implies a cross product and that's not we have here. Actually we have a dot product. You also need to learn about magnetic flux and how it is defined. Flux is not just "Field times area". Only the normal component to the area contributes to the flux.
Does B = B0 + bt^3?
Yes.
 

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