Problem — True or false on induction (1)

Problem

State whether each statement is true (T) or false (F): (a) the emf induced in a loop depends on the change in flux, not on its instantaneous value; (b) Lenz’s law states that the induced current has the same direction as the change in flux; (c) the inductance $L$ of a solenoid depends only on its geometry; (d) in an ideal $LC$ circuit, energy dissipates over a characteristic time $\tau=L/R$.

Solution

(a) T. The Faraday-Neumann-Lenz law gives $\text{emf}=-\ddt{\Phi}$: what counts is the change in flux, not its instantaneous value.

(b) F. Lenz’s law states that the induced current opposes the change in flux that generates it (opposite direction, minus sign in the formula).

(c) T. For a solenoid $L=\dfrac{\mu_0 N^2 A}{\ell}$: it depends only on the number of turns, the area and the length, i.e. on the geometry (and on the core material).

(d) F. An ideal $LC$ circuit has no resistance: there is no dissipation, the energy oscillates indefinitely between $L$ and $C$. The time $\tau=L/R$ is the time constant of an $RL$ circuit.

$\ev{\text{(a) T}\quad\text{(b) F}\quad\text{(c) T}\quad\text{(d) F}}$

Links

Topics: Induzione elettromagnetica Concepts: Legge di Faraday-Neumann-Lenz · Legge di Lenz · Induttanza e autoinduzione · Oscillazioni LC e RLC