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Identify the flux change: Is $B$ varying? Is the area changing? Is the angle changing? This determines which formula to use.

Motional EMF problems: $\varepsilon = Bvl$ for translating rods. $\varepsilon = B\omega l^2/2$ for rotating rods. For rails problems: find EMF, then current ($I = \varepsilon/R_{\text{total}}$), then force ($F = BIl$). Check for terminal velocity conditions.

Faraday's law problems: $\varepsilon = -Nd\Phi/dt$. If $\Phi(t)$ is given, differentiate. If $B(t)$ is given and area is constant: $\varepsilon = -NA\,dB/dt$.

Lenz's law for direction: Determine whether flux is increasing or decreasing, then find the current direction that creates opposing flux using the right-hand rule.

Inductance calculations: Solenoid: $L = \mu_0 N^2 A/l$. Mutual: $M = k\sqrt{L_1 L_2}$ or $M = \mu_0 n_1 n_2 A_{\text{inner}} l$.

Energy: $U = \frac{1}{2}LI^2$. For LC circuits: equate $\frac{1}{2}CV^2 = \frac{1}{2}LI_0^2$ for maximum current.

Common traps: (1) Constant flux means zero EMF (not zero flux). (2) Rotating rod sweeps $l^2\omega/2$ area per second (not $l^2\omega$). (3) Multiple spokes give same EMF as one spoke. (4) Use $n = N/L$ in solenoid inductance. (5) Transformers need AC, not DC.