Magnetic Flux

If you bring N side of magnet towards a solenoid current is ___

If you bring N side of magnet away from a solenoid current is ___

Magnetic Flux

Φ = ABcosθ

• A = area

• θ = angle that loop is tilting away from mag. field

What would change B and Φ ?

Faraday’s Law

emf (ε) is induced when magnetic flux through a loop changed w/ time

Faraday’s Law equation

ε = -N (ΔΦ / Δt)

Lenz’s Law

• I_induced always flows in direction that opposes the change

• If B is increasing (bringing magnet towards coil), B_induced is in opposite direction as B (repelling)

• If B is decreasing (bringing magnet away from coil), B_induced is in same direction as B (attraction)

Right hand rule if bringing magnet towards coil

Right hand rule if bringing magnet away from coil

Conducting Rod

• Conducting Rod completes the circuit. As it falls, the magnetic flux (Φ) decreases and current (I) is induced

• The force due to induced current is upward, slowing the fall

Change in flux (ΔΦ) of rod

ΔΦ = BΔA = B(L*vΔt)

• v*Δt would give meters

Induced emf

|ε| = BvL

Electric field caused by motion of the rod (E)

E = Bv

• v = velocity

If a rod moves at constant speed, external force must be exterted on it:

F_external = ILB

F_external = (B²vL²) / R

R = resistance?

• Equal magnitude and opposite direction to F_magnetic

Mechanical Power from F_external

P_mechanical = (B²v²L²) / R

• Same case for electric power in light bulb

What does an electrical generator do?

What does an electrical motor do?

Induced emf (ε) in rotating coil

ε = NBAωsinωt

Inductance L (not length!)

tells us how much emf (ε) will be induced for a given ROC in current (I)

|ε| = L |ΔI/Δt|

L = N |ΔΦ/ΔI|

Inductance circuit

Current (I) and magnetic field (B) increasing w/ time when switch closed

Inductance of a Solenoid

L=μ₀n²A𝓵

n = N/L

𝓵 = length

RL circuits

when switch closed: current (I) increases, but slows as time goes on and potential difference across inductor decreases

Time constant (𝜏)

𝜏 = L/R

Energy stored in magnetic field

• energy input to establish current in inductor

U = ½ LI²

Magnetic Energy stored in solenoid

U = (B²A𝓵) / (2μ₀)

Transformers

• Applying Faraday’s Law of Induction in both coils

• Power in both circuits must be same

• If Voltage decreases, Current increases

(V_p/V_s) = (N_p/N_s) = (I_s/I_p)