Electric field and potential 


F_{12} = (k_{e}q_{1}q_{2}/r_{12}^{2})
(r_{12}/r_{12}). 
 Electrostatic field of a point charge:

E = (k_{e}q/r^{2})
(r/r). 

Φ_{e(through closed surface)} = Q_{inside}/ε_{0}. 
 Electrostatic potential energy:

∆U = U_{B}  U_{A} = q ∫_{A}^{B}E·dr. 
 Electrostatic potential difference:

∆V = ∆U/q 
 The potential of a point charge:

V(r) = kq/r
(convention: V = 0 at infinity.) 

E_{x} = dV/dx, E_{y} = dV/dy, E_{z} =
dV/dz 
Capacitors 


C = Q/V 
 Parallel plate capacitor:

C = εA/d 
 Energy stored in a capacitor:

U = ½(Q^{2}/C) = ½CV^{2} 

1/C = (1/C_{1})
+ (1/C_{2}) + (1/C_{3}) 

C = C_{1
}+ C_{2 }+ C_{3} 
Currents and circuits



I = ∆Q_{net}/∆t
= ∫j∙dA, j = current density 

R = ∆V/I 
 Resistance of a straight wire:

R = ρL/A 

P = I∆V = I^{2}R = (∆V)^{2}/R 

R = R_{1
}+ R_{2 }+ R_{3} 

1/R = (1/R_{1})
+ (1/R_{2}) + (1/R_{3}) 
 RC circuits time constant:

τ = RC 
Magnetostatics 

 Magnetic force on a moving charge:

F = qv × B 
 Magnetic force on a long straight wire:

F = IL × B 
 Charged particle in a magnetic field:

r = mv/(qB) 

∮_{Γ} B∙ds = μ_{0}I_{through Γ} 
 The magnetic field of a long straight wire:

B = μ_{0}I/(2πr) 
 The magnetic field inside a solenoid:

B = μ_{0}nI 
Current loops 

μ = IAn 

τ = μ × B, τ = μB sinθ 

U_{μ} = μB cosθ 