Cheat Sheet — Midterm 1

PHYS 142 (Summer 2014)

Constants:

k = 9.0× 109 N ·m2/C2 ε0 = 8.9× 10−12 C2/N ·m2 g = 9.8 m/s2

e = 1.6× 10−19 C me = 9.1× 10−31 kg mp = 1.7× 10−27 kg

Electrostatics

General:

~F = q~E

‹A

~E · n dA =Qenc

ε0ΦE =

¨A

~E · n dA u =1

2ε0E

2

Potential:

V = k

ˆdq

r−∆V =

ˆ b

a

~E · d~l ~E = −~∇V = −∂V∂x

ı− ∂V

∂y− ∂V

∂zk

Point Charges:

~F =kq1q2r2

r ~E =kq

r2r V =

kq

rU = k

∑i<j

qiqjrij

Dipoles:~p = q~d ~τ = ~p× ~E U = −~p · ~E

Dielectrics:

ε = Kε0

‹A

~E · n dA =Qenc-free

εu =

1

2εE2 σi =

(1− 1

K

)Electrical Circuits

Current:I =

dQ

dt= n|q|vdA ~J = nq~vd ρ =

E

J

Capacitors:

C =Q

V

1

Ceq=

n∑i=1

1

Ci(Series) Ceq =

n∑i=1

Ci (Parallel) U =1

2CV 2 =

Q2

2C

Resistors:V = IR R =

ρL

A

Circuits:

V = E − Ir P = IV = I2R =V 2

R