Formulas For Calculus-based Physics 2

Calculus-Based Physics II by Jeffrey W. Schnick q1 q2 r2

F =k







F = qE

E=

kq r2

U = qϕ

τ = µ ×B

µ = N IA






1 1 1 = + f o i

FB = ∇(µ ⋅ B)







F = I L×B




M=

F = q v ×B

M =−




B=

ϕ = Ed

µo 3 (µ ⋅ rˆ) rˆ − µ 4π r3







µo I 2π r

W = − q ∆ϕ

B=

kq ϕ= r




E = v ×B

⋅

B = − µ o eo vP × E




V = IR L R=r A P =IV R s = R1 + R 2 1 Rp = 1 1 + R1 R 2





Φ B = B ⋅ dA

ΦB = B ⋅ A







E = N ΦB

⋅

E=

1 ⋅ ΦB 2π r

E = E MAX sin( 2πf t ) mλ = d sin θ (m + 12 ) λ = d sin θ E RMS = 12 E MAX Csc =

Q Q ,C= ϕ V

mλ = w sin θ mλ 2 = 2t

U = CV A C = κ eo d 1 Cs = 1 1 + C1 C 2

(m + ) λ 2= 2t n λ 2 = 1 λ1 n2

C p = C1 + C 2

c n= v n1 sin θ 1 = n2 sin θ 2 n sin θ c = 2 n1

1 2

2

τ = RC V = E (1 − e −t / τ ) V = Vo e − t / τ I = I o e −t / τ

h' h i o

E = − ∇ϕ

1 f P = P1 + P2 P=




Φ E = E ⋅ dA




 1 1 1   = (n − no )  + f R R 2   1

P

I =Q

dq = λ dx k dq dE = 2 r k dq dϕ = r
F = −∇U

o

4π



x sin 2 x 2 ∫ (cos x) dx = 2 + 4 dx 1 + sin x ∫ cos x = 12 ln 1 − sin x dx ∫ (cos x) 2 = tan x dx 2 2 ∫ x 2 + a 2 = ln x + x + a xdx 2 2 ∫ x2 + a2 = x + a

(

∫

x +a 2

1 2

I = I o (cosθ ) 2




µ I dl × r dB =

∫ (cos x) dx = sin x

x 2 dx

=

2

(

∫

∫

dx (x2 + a2 ) xdx

3

(x + a ) 2

2

= 2

3

=− 2

x 2 dx (x2 + a 2 )

3

1 a2

=− 2




E B ⋅ dl = µ o ITHROUGH + µ 0 e 0 Φ
Q E ⋅ dA = ENCLOSED eo

)

(

x2 + a2 1 x + a2

ln x + x + a

1 e = 1.60 × 10 −19 C k=

1 4π e o

N ⋅ m2 C2 C2 −12 eo = 8.85 × 10 N ⋅ m2 T⋅m µ o = 4π × 10 − 7 A nH 2 O = 1.33 k = 8.99 × 109

me = 9.11 × 10−31 kg

2

2







x

x2 + a2







)

x

r3


B E ⋅ dl = − Φ
B ⋅ dA = 0

x 2 x + a2 − 2

a2 ln x + x 2 + a 2 2

∫




mp = 1.6726 × 10−27 kg

+ 2

)

c = 3.00 × 108

m s

N A = 6.022 × 1023

particles mole