electromagnetism Flashcards
E.M.F equation
ε = ∮𝒇 ⋅dl
ε: e.m.f
𝒇: force per unit charge (= -E)
its the total change in electric potential around a closed loop
what happens when a metal bar is pulled through a magnetic field
the positive and negative charges experience a force in opposite directions (F = Bqv) so they are separated. this happens until the resulting electric field balances the magnetic field (Eq = Bqv)
whats magnetic flux
Φₘ = ∫B⋅dA
What’s Faraday’s law
A changing magnetic flux produces an e.m.f (induced e.m.f)
ε = - dΦₘ/dt = - d/dt ∫B⋅dA
ε: induced e.m.f
Φₘ: magnetic flux
t: time
What’s Lenz’s law
The direction of e.m.f induced by Faraday’s law is such that the current produced creates a magnetic field that opposes the change in flux
what’s the 4th Maxwell equation
combines
ε = - dΦₘ/dt = - d/dt ∫B⋅dA (induced e.m.f)
with
ε =∮E⋅dl (potential equation)
gives:
∮E⋅dl = - d/dt ∫B⋅dA
hence a changing B-field produces an E-field
What’s an eddy current
loops of current in an extended conducting surface that form when it’s pulled through a magnetic field. (i.e current isn’t confined to a wire)
what’s Maxwell’s correction to Ampere’s law
For a capacitor, the space between the plates has no current so Ampere’s law didn’t work. Maxwell invented the idea of displacement currents (changing E-field is treated as a current)
since E = Q/ε₀A
Q= ε₀AE
I = dQ/dt = ε₀A ∂E/∂t
∴∮B⋅dl = µ₀ (I + ε₀A ∂E/∂t )
or ∮B⋅dl = µ₀ * ∫(j + ε₀∂E/∂t )⋅dA
j: current density vector
what’s the significance of Maxwell’s corrections to Ampere’s law
- introduced the idea of displacement currents. Changing E-fields act like a current.
- the equation of the M-A law suggests that a changing E-field gives rise to a magnetic field
How can EM radiation be predicted?
using Maxwell-Ampere law and Faraday’s law:
M-A law:
∮B⋅dl = µ₀ * ∫(j + ε₀∂E/∂t )⋅dA
a changing E-field produces a B-field
Faraday’s law:
∮E⋅dl = - d/dt ∫B⋅dA
a changing B-field produces an E-field
hence its possible this is a self-sustaining process
