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Faraday law of induction Lenz’s rule Induced currents and voltages B field changes as we move permanent magnet Area decreases as we stretch! Induced current and voltages are generated when B field through the loop or area of the loop in B field is changing. Changes in magnetic flux Φ=ΒΑ is what controls the effect. Concept of magnetic flux, I Φ = ( B cos φ ) A; Unit: Φ = ( B ⋅ A) Weber (Wb) I Wb = 1T m2 Tesla Wilhelm Weber, Germany 1804-1891 A A A Example: B B B 4 Concept of a vector for AREA of a current loop A directed perpendicular to the surface trough which the current flows. Polarity of the direction is according to the “screw” rule – if you put a screw into the surface, the direction of its “penetration” is the direction of vector A 5 Faraday’s law of induction British physicist and chemist (1791-1867) ∆Φ E = −N ∆t Φ = ( B ⋅ A) = for considered problems = BA N=number of coil turns A=area of the coils Wb T ⋅ m 2 N m 2 Nm Units: = = ⋅ = = Volt , b / c s s C (m / s) s C N V = E ⋅ d and Volt = m C Lenz’s rule The induced emf has polarity that leads to induced current whose direction is to oppose the original flux Φ change Baltic German, Worked at the U of St. Petersburg, Russia Motional emf Em = L V B Fq = qE = qE / L = q ⋅ vel ⋅ B ⇒ E = L ⋅ vel ⋅ B Charge separation Magnetic force DC generator Motional emf through Faraday’s law of induction Em = L V B Em = ∆Φ ∆t B∆A BL∆x = =LVB = ∆t ∆t ∆X V L B Current should flow CW to provide ∆B opposite to the background B. Motional emf should have plus terminal at the bottom Motional emf for tilted B field Em = L V⊥ B B∆A cos θ BL∆x cos θ E= = = = L V⊥ B m ∆t ∆t ∆Φ ∆t Current Area B field θ ∆X ∆x V L B θ V⊥ x Sliding rod, magnetic friction: Acceleration Deceleration and stationary motion with constant velocity Problem: Sliding rod A conducting rod slides down between two frictionless vertical copper tracks at a constant speed of 4 m/s perpendicular to a 0.5 T magnetic field. The resistance of the rod and tracks is negligible. The rod maintains electrical contact at all times and has a length of 1.3 m. A 0.75 ohm resistor is attached between the tops of the tracks. What is the mass of the rod? The rod is actually working as a DC generator. What is the efficiency of mechanical energy conversion to electrical energy? η 2 electrical power delivered I R = mechanical power supplied mgV Solution,1 Solution,2 Induced effect: polarity Problem: Sliding coil A rectangular coil has N=60 turns and resistance of R=0.02 ohms. When it is pulled downward, out of magnetic field at a speed of 8 m/s, a current of I=0.2 A flows in this coil. 1) What is the direction of induced current? 2) Determine the strength of the magnetic field. × × × × × × × × × × × × × B× × × × × L2=8 cm × × × × × × × × × × × × × L1=20 cm × × × × × V=8 m/s × × × × × × × × × × × × × × × × × × × × × × × × Solution for sliding coil × × × × × × L2=8 cm × × × × × × × × × B× × × × × × × × × × × × × × × L1=20 cm V=8 m/s Application: Induction stove Water is boiled in the pot made of conducting ferromagnetic material b/c AC voltage under the panel creates alternative magnetic field in nearby space including the bottom of the pot. Induced voltage creates electric current that heats the pot Discussion questions Discussion questions Discussion questions Summary of equations ∆Φ E = −N ∆t Em = L V B Φ = BA
