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Electromagnetism Cheat Sheet
Electrostatics
Q: particle charge [C] r: relative permittivity [1]F: force [N]
E: electric field [N/C]0: vacuum permittivity U: electric potential
[J/C]
= 8.85 1012 C2Nm2
W: work [J]
Coulombs law F= 1
40r
Q1Q2r2
Electric field of a point charge Q E= 1
40r
Q
r2
Electric potential around a point charge Q U= 1
40r
Q
r
Force exerted by an electric field on a point charge Q F =QE
Work done by an electric field on a point charge Q W = Q(U2
U1)
Relationship between electric field intensity and potential E=
dUds
Electric circuits
R: resistance [] l: length of the wire segment [m]: resistivity
[m] A: cross-sectional area of the wire [m2]U: voltage [V]I:
current [A]
Resistance of a homogeneous wire R=
l
A
Equivalent resistance of resistors connected in series Req= R1+
R2+ R3+ . . .
Equivalent resistance of resistors connected in parallel R1eq
=R11 + R
12 + R
13 + . . .
Ohms law* R=U
I, *=
E
J
Work done in a DC circuit* W =U It= I2Rt=U2
R
t
Electrical power in a DC circuit P =U I=I2R=U2
R
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Kirchhoffs junction rulej
Ij = 0
Kirchhoffs loop rulej
Uj = 0
AC circuits
X: reactance [] Z: impedance []: angular frequency [rad/s] :
phase angle [rad]L: self-inductance [H]C: capacitance [F]
Effective (root mean square) voltage and current in an
AC circuit (sinusoidal time-dependence)
Urms=Umax
2, Irms=
Imax
2Inductive reactance XL= L
Capacitive reactance XC= 1
C
Magnitude of impedance in an L-R-C series circuit Z=
R2 + (XL XC)2
Magnitude of impedance in a parallel L-R-C circuit 1
Z
= 1
R2
+ 1
XL
1
XC2
Phase angle cos=R
Z
Moving charges in a magnetic field
q: particle charge [C] r: helix/circle radius [m]B: magnetic
field [T] m: particle mass [kg]v: velocity of the particle [m/s] f:
cyclotron frequency [Hz]
: angle between the magnetic field and I: current [A]the
particles velocity [rad] M: torque [Nm]
Force exerted by the magnetic field on a charge F= qv B
F=qvB sin
Radius of the helix/circle the charge follows r=mv
qBsin
Cyclotron frequency (frequency of the circular motion) f= qB
2m
Magnitude of the force exerted by the magnetic field ona
current-carrying straight wire of length l
F =I lB sin
