ε = – N dφ/dt However, the equation does not state anything about the conservation of energy. Lenz’s Law can explain energy conservation and the negative sign in Faraday’s Law equation.
What is Lenz’s Law
Lenz’s Law and Conservation of Energy
Applications of Lenz’s Law
Example Problems and Solutions
“The polarity of the induced emf is such that it opposes the change in magnetic flux that produced it.” When a magnetic field induces a current in a conducting coil, the induced current generates its magnetic field, opposite to the inducing magnetic field. In other words, an induced current will always oppose the motion that started it in the first place. Lenz’s Law is significant since it can determine the direction of the induced current and the magnetic field induced by the current. The change in the magnetic flux around a conducting coil may be caused in several ways:
Change the magnetic field strengthMove the magnet toward or away from the coilMove the coil into or out of the magnetic fieldRotate the coil relative to the magnet
Lenz’s Law is named after German physicist Heinrich Friedrich Lenz after he deduced it in 1834. Suppose the current did not oppose the magnet’s magnetic field. Then, the induced magnetic field would be in the same direction as the inducing magnetic field. These two magnetic fields would add up and create a larger magnetic field. This larger magnetic field would induce another current in the coil twice the magnitude of the original current. This induced current will generate another magnetic field, and the process will continue. Thus, an endless loop of induced currents and magnetic fields would violate the energy conservation law. Therefore, Lenz’s Law is a consequence of the energy conservation principle.
InductorElectric generatorsElectromagnetic brakingInduction cooktopEddy current equalizersEddy current dynamometersMicrophonesCard readers
Solution: Given, N = 1 r = 5 cm = 0.05 m A = πr2 = π (0.05m)2 = 0.0079 m2 Δt = 0.2 s (B cos θ)initial = 0.1 T (B cos θ)final = 0.5 T ΔB = (B cos θ)final – (B cos θ)initial = 0.5 T – 0.1 T = 0.4 T From Faraday’s law, |ε| = N Δφ/Δt or, |ε| = N A Δ(B cos θ)/Δt or, |ε| = 1 x 0.0079 m2 x 0.4 T/0.2 s = 0.016 Tm2/s = 16 mV Problem 2: A circular coil of wire with 450 turns and a radius of 8 cm is placed horizontally on a table. A uniform magnetic field pointing directly into the wire and perpendicular to its surface is slowly turned on, such that the strength of the magnetic field can be expressed as a function of time as B(t) = 0.01(Ts-2) x t2. (A) What is the total emf in the coil as a function of time? (B) In which direction does the current flow? Solution: Given, B(t) = 0.01(Ts-2) x t2 N = 450 r = 8 cm = 0.08 m A = πr2 = π(0.08 m)2 = 0.02 m2 From Faraday’s law, ε = – N dφ/dt or, ε = – 450 x d(BA)/dt or, ε = – 450 x 0.02 m2 x d (0.01(Ts-2) x t2)/ dt or, ε = – 0.09 x 2t Tm2/s2 or, ε = – 0.18t T/s (B) The current will be clockwise looking from the top.
