$∣ E (r) ∣ = \frac{q}{4 π ε_{0} r^{2}}$	$∣ E (r) ∣ = \frac{λ}{2 π ε_{0} r}$	$∣ E ∣ = \frac{σ}{2 ε_{0}}$

$V (r) = \frac{q}{4 π ε_{0} r}$	$V (r) = - \frac{λ}{2 π ε_{0}} ln r$	$V (x) = C - \frac{σ}{2 ε_{0}} x$

$\oint_{S} E \cdot \hat{n} d A = \frac{Q_{i n S}}{ε_{0}}$	$Δ V = \frac{Q}{C}$	$E = ρ J$

$∣ J ∣ = \frac{I}{A}$	$U = \frac{Q^{2}}{2 C}$	$R C = ε_{0} ρ$

$F = q v \times B$	$R = \frac{m v}{q B}$	$d B = \frac{μ_{0}}{4 π} I d ℓ \frac{t \times r}{r^{3}}$

$V (b) - V (a) = - \int_{a}^{b} E \cdot d r$	$R = \frac{ρ L}{A}$	$C = \frac{κ ε_{0} A}{d}$

$\frac{d F}{d ℓ} = I t \times B$	$\oint_{C} B \cdot d r = μ_{0} I_{C}$	$B = \frac{μ_{0} q}{4 π} \frac{v \times r}{r^{3}}$

$C_{p a r a l l e l} = C_{1} + C_{2}$	$\frac{1}{C_{s e r i e s}} = \frac{1}{C_{1}} + \frac{1}{C_{2}}$	$tan θ = \frac{sin θ}{cos θ}$

$B = \nabla \times A$	$A (r) = \frac{μ_{0}}{4 π} \int \frac{I d ℓ t}{r}$	$U = - m \cdot B$

${(x - x_{c})}^{2} + {(y - y_{c})}^{2} = R^{2}$	$E_{x} = - \frac{\partial V}{\partial x}$	$E_{y} = - \frac{\partial V}{\partial y}$

$Q = ρ \cdot V o l$	$Q = σ A$	$σ (x) = ε_{0} E (x) \cdot n$

$F_{x} = - \frac{\partial U}{\partial x}$	$N = p \times E$	$p = \sum_{i = 1}^{2} q_{i} r_{i}$

$\frac{d}{d u} {tan}^{- 1} u = \frac{1}{1 + u^{2}},$	$\frac{d}{d x} \frac{u}{v} = \frac{u^{'} v - v^{'} u}{v^{2}}$	$\frac{d}{d x} ln x = \frac{1}{x}$

$\int_{a}^{b} \frac{d r}{r^{2}} = \frac{1}{a} - \frac{1}{b}$	$\int_{a}^{b} \frac{d r}{r} = ln \frac{b}{a}$	$tan ({tan}^{- 1} (x)) = x = {tan}^{- 1} (tan (x))$

$Δ W = Δ (q V)$	$\frac{d W}{d V o l} = \frac{1}{2} ε_{0} κ E^{2}$	$W = \frac{Q^{2}}{2 C} = \frac{C V^{2}}{2}$

$ln (e^{x}) = - ln (e^{- x}) = x$	$V = I R$	$m a = - k x$

$V o l = π r^{2} h$	$V o l = \frac{4 π}{3} r^{3}$	$V o l = L W H$

$A r e a = 2 π r h$	$A r e a = 4 π r^{2}$	$A r e a = L^{2}$

$C = \frac{4 π ε_{0} a b}{b - a}$	$C = \frac{2 π ε_{0} ℓ}{ln \frac{b}{a}}$	$C = \frac{ε_{0} A}{d}$

$∣ E_{t o t a l} ∣ = \frac{∣ E_{e x t} ∣}{κ}$	$J = \frac{I}{A} \hat{n}$	$\frac{d y}{d x} = \frac{E_{y}}{E_{x}}$

$\frac{d}{d x} {tan}^{- 1} f (x) = \frac{f^{'} (x)}{1 + f^{2} (x)}$	$tan (a - b) = \frac{tan a - tan b}{1 + tan a tan b}$	$∣ B ∣ = \frac{μ_{0} I}{2 π R}, \frac{μ_{0} I}{2 R}, μ_{0} n I,$

$\int_{a}^{b} \frac{d x}{{(c - x)}^{2}} = \frac{a - b}{(c - a) (c - b)}$	$U = \frac{1}{2} C V^{2}$	$Q = λ ℓ$

$\frac{1}{4 π ε_{0}} = 9.0 \times 1 0^{9} \frac{N m^{2}}{C^{2}}$	$μ_{0} = 4 π \times 1 0^{- 7} \frac{T m}{A}$	$c = 3.0 \times 1 0^{8} \frac{m}{s}$

A region of space around the origin contains an electric ﬁeld

E = 4.0 \frac{N}{m \cdot C} x i + 3.0 \frac{N}{C} j

. Such a ﬁeld cannot exist in empty space. Find the total charge within a cube of side

a = 0.5 m

centered on the origin, with its six faces possessing normals in the six cardinal directions

\pm i, \pm j, \pm k

Physics 202 Exam 2, Name:

1 (p-73) (5+5+5 points)

2 (p-76) (10 points)

3A. (p-109) (5+3 points)

B. (p-100) (5 points)

C. (e-49) (6 points)

4 A. (p-131) (2+2+2+2+2 points)

B. (p-127) (2+2+2+2+2 points)

5 A. (e-58) (5+5 points)

B. (p-104) (6 points)

6A. (p-84) (5+5 points)

B. (p-118) (3+3+4 points