Physics 2 Equations Sheet with ALL Equations

Gravity
!" "
• Gravity Force: 𝐹 = #!" "
• 𝐺 = 6.67 ∗ 10$%% Nm2/kg2

Kinematic Equations
• 𝑣& = 𝑣' + 𝑎𝑡
• 𝑥& = 𝑥' + 𝑣̅ 𝑡
(# )($
• 𝑣̅ = *
%
• 𝑥& = 𝑥' + 𝑣+ 𝑡 + * 𝑎𝑡 *
• 𝑣& * = 𝑣' * + 2𝑎(𝑥& − 𝑥' )
• Returning to 𝑥' , 𝑣& = −𝑣'

Electricity
, |. ." |
• Coulomb’s Law: 𝐹 = #!"
• 𝑘 = 8.99 ∗ 10/ Nm2/C2
• 𝑒 = ±1.602 ∗ 10$%/ C
%
• ∈' = 01, = 8.85 ∗ 10$%*
.%&'
• .&(&)'*+%
= 𝑒𝑥𝑐𝑒𝑠𝑠 𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑛𝑠
• 𝑒𝑥𝑐𝑒𝑠𝑠 𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑛𝑠 ∗ 𝑚23245#+6 = ∆𝑚
• 𝑚23245#+6 = 9.109 ∗ 10$7% kg
• 𝑚8#+5+6 = 1.67 ∗ 10$*9 kg

Electric Field
• No E field within an object
,: "
• 𝐹= #"
= 𝑚𝑎 = 𝑞𝐸 = −𝑒𝐸
,.! ;
• 𝐸= #"
=:
o Fields all inwards = E –
.
• Point charge (far): 𝐸 = 01∈ # "
$
= .
• Infinite sheet (close): 𝐸 = *> = *>
$ $?
• Direction partial: SOHCAHTOA
@
• Direction trig: 𝜃 = tan$% (@, )
-
• Magnitude partial: 𝑎* + 𝑏 * = 𝑐 *
,. ,.
• X-component: 𝐸A = 4 " 𝑐𝑜𝑠𝜃32&5 − 4 "
𝑐𝑜𝑠𝜃#BCD5
(&#' *./0'
,. ,.
• Y-component: 𝐸E = 4 "
𝑠𝑖𝑛𝜃32&5 − 4 "
𝑠𝑖𝑛𝜃#BCD5
(&#' *./0'


• Magnitude trig: 𝐸 = L𝐸A * + 𝐸E *
• Number of lines: 𝑁 = 𝑘𝑞

, F ,:
• Density of lines: 01# " = 01# "
;⃗
• Test charge: 𝐸N⃗ = :
• Repulse: Q1 & Q2 same sign, Qnet +
• Attract: Q1 & Q2 opposite sign, F -

Dipole Moment
• 𝑝⃗H" I = 6.17 ∗ 10$7' C*m
• ℓH K+6L = 1.97 Å
• 𝑝 = 𝑄ℓ
,*8
• 𝐸 = #1
• 𝜏 = 𝑄ℓ𝐸𝑠𝑖𝑛𝜃 = 𝑝𝐸𝑠𝑖𝑛𝜃
• 𝜏 = 𝐹 ∗ 𝑎𝑟𝑚MLN
• 𝑈 = −𝑝𝐸𝑐𝑜𝑠 𝜃
• ∆𝑈 = −𝑊 = −𝑞𝐸𝑑
• 𝑊 = 𝑝𝐸W𝑐𝑜𝑠𝜃' − 𝑐𝑜𝑠𝜃& X = 𝐹𝑑 = 𝑞𝐸𝑑
• 𝜃∥ = 360°; 𝜃∦ = 180°
,8
• Resultant E field: 𝐸A = (L" )ℓ" )1/"
• 𝐸625 = 2𝐸𝑠𝑖𝑛𝜃
,8
• If 𝑑 ≫ 𝐿, 𝐸 = L1 and 𝑑 = 𝑟
, |.! ." | % %
• 𝐹625 = 𝐹% + 𝐹* … = 3%.' )+%5&*6.+% V"
+ # " + # " ..
T%∗%' ! "

o Keep r unconverted
o Same charge element, -F
• Power Laws of E-Fields
Systems of Charges E-Field Reduction in field at 2r
Monopole (n=1) 1 Factor of 4
𝐸∝
𝑟*
Dipole (n=2) 1 Factor of 8
𝐸∝ 7
𝑟
Quadrupole (n=4) 1 Factor of 16
𝐸∝ 0
𝑟
Neutral object (n=30) 1 Factor of 120
𝐸 ∝ WXY (06)
𝑟

Electric Flux
• Flux: Φ@ = 𝐸𝐴𝑐𝑜𝑠𝜃 = 𝐸N⃗ ∗ 𝐴⃗ = 4𝜋𝑘𝑞
• Φ265#E = − ; Φ2AB5 = +
• ΦZ[\ only depends on charge of 𝑄264
• 𝜃32&5 = 180 ; 𝜃#BCD5 = 0
.&%)
• Gauss’s Law: Φ@ = ∈$
= 4𝜋𝑘𝑄264 = 𝐸(4𝜋𝑟 * )