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Equation Sheet for Exam Preparation - Electricity and Magnetism | PHYS 132, Study notes of Physics

Material Type: Notes; Class: Electricity & Magnetism; Subject: Physics; University: Lafayette College; Term: Fall 2005;

Typology: Study notes

Pre 2010

Uploaded on 08/19/2009

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Phys 132 Equation Sheet Fall 2005
Electric Forces and Fields: ~
E=1
4π0
q
r2ˆr~
F0=q0~
E~
E=1
4π0X
i
qi
r2
i
ˆri
ΦE=I~
E·d~
AΦE=Qin
0
~τ =~p×~
E U =~p·~
EInfinite sheet: E=η
20
Electric Potential: V=1
4π0
q
rU=q0V V =1
4π0X
i
qi
ri
V=1
4π0Zdq
r
VfVi=Zf
i
~
E·d~s Es=dV
ds ~
E=−∇V=ˆ
i∂V
∂x +ˆ
j∂V
∂y +ˆ
k∂V
∂z
Capacitance: C=Q
Vc
C=0A
d
1
Cseries
=1
C1
+1
C2
+1
C3
+···
Cparallel =C1+C2+C3+·· · U=1
2QV u =1
20E2=K0
Circuits: I=dQ
dt V=IR P =I(∆V)Rseries =R1+R2+R3+···
1
Rparallel
=1
R1
+1
R2
+1
R3
+··· τ=RC q =Q0et/τ
Magnetic Forces and Fields: ~
F=q~v ×~
B d ~
F=Id~
l×~
B ~τ =~µ×~
B U =~µ ·~
B
µ0Iencl =I~
B·d~s d ~
B=µ0
4π
Id~
l׈r
r2Long straight wire: B=µ0I
2πr
Center of current loop: B=µ0I
2rLong solenoid: B=µ0nI
Induction: ΦB=Z~
B·d~
A ε =dΦB
dt VL=Ldi
dt UL=1
2LI2uB=B2
2µ0
τ=L/R ω =1
LC I~
E·d~
l=dΦB
dt I~
B·d~
l=µ0ic+0
dΦE
dt encl
Electromagnetic Waves: ~
F=q(~
E+~v ×~
B)vem =c= 1/0µ0
E(x, t) = ˆ
jEmax sin(kx ωt)B(x, t) = ˆ
kBmax sin(kx ωt)k=2π
λω= 2πf
c=λf E =cB ~
S=1
µ0
(~
E×~
B)I=I0cos2θ
AC Circuits: v(t) = Vcos(ωt +φ)Vrms =V /2XC= 1/ωC XL=ωL
Z=qR2+ (XLXC)2Pave =Vrms Irms cos φ
Kinematics: v=v0+at x =x0+v0t+1
2at2v2=v2
0+2a(xx0)ar ad =v2
r
Vectors: Ax=Acos θ Ay=Asin θ A =qa2
x+A2
y~
A·~
B=AB cos φAB
~
A·~
B=AxBx+AyBy+AzBz~
A×~
B= ˆnAB sin φAB
Math: ax2+bx +c= 0 x=b±b24ac
2a(1 + x)n1 + nx for x1
Constants: e= 1.602 ×1019 C0= 8.85 ×1012 C2/Nm2
µ0= 4π×107N/A2me= 9.109 ×1031 kg c= 3.00 ×108m/s
1
pf2

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Phys 132 Equation Sheet Fall 2005

Electric Forces and Fields:

E =

4 π 0

q

r

2

F

0

= q 0

E

E =

4 π 0

i

qi

r

2

i

r ˆ i

E

E·d

A Φ

E

Qin

0

~τ = ~p×

E U = −~p·

E Infinite sheet: E =

η

0

Electric Potential: V =

4 π 0

q

r

U = q 0

V V =

4 π 0

i

q i

r i

V =

4 π 0

dq

r

V

f

− Vi = −

∫ f

i

E · d~s Es = −

dV

ds

E = −∇V = −

(

i

∂V

∂x

  • ˆj

∂V

∂y

k

∂V

∂z

)

Capacitance: C =

Q

∆Vc

C =

 0 A

d

Cseries

C 1

C 2

C 3

Cparallel = C 1 + C 2 + C 3 + · · · U =

QV u =

 0 E

2

 = K 0

Circuits: I =

dQ

dt

∆V = IR P = I(∆V ) R

series

= R

1

+ R

2

+ R

3

Rparallel

R 1

R 2

R 3

  • · · · τ = RC q = Q 0

e

−t/τ

Magnetic Forces and Fields:

F = q~v ×

B d

F = Id

B ~τ = ~μ×

B U = −~μ·

B

μ 0 Iencl =

B · d~s d

B =

μ 0

4 π

Id

l × rˆ

r

2

Long straight wire: B =

μ 0

I

2 πr

Center of current loop: B =

μ 0

I

2 r

Long solenoid: B = μ 0 nI

Induction: ΦB =

B · d

A ε = −

dΦ B

dt

∆VL = −L

di

dt

UL =

LI

2

uB =

B

2

2 μ 0

τ = L/R ω =

LC

E · d

l = −

dΦ B

dt

B · d

l = μ 0

(

i c

0

dΦ E

dt

)

encl

Electromagnetic Waves:

F = q(

E + ~v ×

B) vem = c = 1/

 0 μ 0

E(x, t) = ˆjE max

sin(kx − ωt) B(x, t) =

kB max

sin(kx − ωt) k =

2 π

λ

ω = 2πf

c = λf E = cB

S =

μ 0

E ×

B) I = I

0

cos

2 θ

AC Circuits: v(t) = V cos(ωt + φ) V rms

= V /

2 X

C

= 1/ωC X L

= ωL

Z =

R

2

  • (X L

− X

C

2 P ave

= V

rms

I

rms

cos φ

Kinematics: v = v 0

+at x = x 0

+v 0

t+

at

2 v

2 = v

2

0

+2a(x−x 0

) a rad

v

2

r

Vectors: A x

= A cos θ A y

= A sin θ A =

a

2

x

+ A

2

y

A ·

B = AB cos φ AB

A ·

B = AxBx + AyBy + Az Bz

A ×

B = ˆnAB sin φ AB

Math: ax

2

  • bx + c = 0 x =

−b ±

b

2 − 4 ac

2 a

(1 + x)

n

≈ 1 + nx for x  1

Constants: e = 1. 602 × 10

− 19

C  0

= 8. 85 × 10

− 12

C

2

/Nm

2

μ 0

= 4π × 10

− 7 N/A

2 m e

= 9. 109 × 10

− 31 kg c = 3. 00 × 10

8 m/s

Extras: ε = vBL P =

F · ~v

dx

(x

2 ± a

2 )

3 / 2

±x

a

2 (x

2 ± a

2 )

1 / 2

xdx

(x

2 ± a

2 )

3 / 2

(x

2 ± a

2 )

1 / 2

dx

(x

2 ± a

2 )

1 / 2

= ln(x +

x

2 ± a

2 )

xdx

(x

2 ± a

2 )

1 / 2

= (x

2

± a

2

)

1 / 2