Force on a current-carrying conductor in a magnetic field

$$F = BIl \qquad (\text{conductor perpendicular to the field})$$

Electromagnetic induction

$$\text{Induced e.m.f.} = -N\frac{\Delta\Phi}{\Delta t}\ (\text{Faraday's law; Lenz: opposes the change}) \qquad E = Blv \ \text{(straight conductor moving across a field)}$$

Transformer

$$\frac{V_s}{V_p} = \frac{N_s}{N_p} \qquad \text{Ideal: } V_pI_p = V_sI_s$$ $$\text{Efficiency} = \frac{V_sI_s}{V_pI_p}\times 100\%$$

• Step-up: $N_s > N_p$ (voltage increases, current decreases). Step-down: $N_s < N_p$.

Power transmission

$$\text{Power loss in cables} = I^2R \qquad I = \frac{P}{V}$$ Transmitting at a high voltage reduces the current and therefore the power loss.

A.C.

$$V_{\text{rms}} = \frac{V_0}{\sqrt{2}} \qquad I_{\text{rms}} = \frac{I_0}{\sqrt{2}} \qquad f = \frac{1}{T}$$