# List of formulas related to magnetism

## Magnetic Flux Through The Open Surface S

B: magnitude of the magnetic field (T, tesla), α: angle between B and perpendicular line to surface S.

$$\phi = BS cos \alpha (Wb, W eber)$$

### Magnetic Forces On Moving Charges

v: velocity of the charge (m/s)

$$\alpha = (\vec{B}, \vec{v})$$ $$f = |q|vB sin \alpha$$

### Force On A Current Carrying-Wire

I: current (A), l: length of the wire (m)

$$F = BIl sin \alpha$$

### Force Between Two Parallel Current-Carrying Wire

r: distance between two wires (m)

$$F = 2.10^{-7} \frac{I_1 I_2}{r} l$$

### Magnetic Field Of A Long Current Charge Wire

r: perpendicular distance from the center of the wire (m)

$$B = 2.10^{-7} \frac{I}{r}$$

### Magnetic Field Of A Loop

N: numbers of turns per unit length of solenoid (turns/m)

$$B = 4 \pi 10^{-7} nI$$

### Induced Electromotive Force- Faraday's Law

N: numbers of turns per loop (turns/m)

$$\xi _C = - N \frac{\Delta \phi}{\Delta t}$$

### Inductance

$$L = \frac{\phi }{i} (H, H enry)$$ $$\phi = Li (Wb)$$ $$\xi _C = \frac{\Delta \phi}{\Delta t} = -L |\frac{\Delta i}{\Delta t}|$$

### Electric Energy

$$W_c = \frac{1}{2}Cu^2$$

### Magnetic Energy

$$W_L = \frac{1}{2}Li^2$$

### Electric-Magnetic Energy

$$W = W_c + W_L = \frac{1}{2C}q_0 ^2$$