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Electromagnetism Study Notes for GRE Physics, Study notes of Electromagnetism and Electromagnetic Fields Theory

Massachusetts Institute of Technology (MIT)Electromagnetism and Electromagnetic Fields Theory

An overview of electromagnetism, including topics such as electricity, magnetism, capacitors, and Maxwell's equations. It includes equations and formulas related to each topic, as well as explanations of key concepts. The document also provides tips for taking the GRE in SI units and notes on differences in Maxwell's equations. It could be useful as study notes or a summary for students studying electromagnetism.

Typology: Study notes

2022/2023

Uploaded on 05/11/2023

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1 Electromagnetism
General comments: the GRE is in SI units, so for those who took 8.022, make sure to
pay attention to where the epsilons and mus go. (And thus the slightly different form of
Maxwell’s Equations.)
Also, on one of the practice tests I looked at, they asked about which if Maxwell’s equa-
tions would need to be modified to account for magnetic monopoles.
Work: W
q0has units of volts. Volt = Joules/Coulomb.
1.1 Electricity
k = 1
4πε0[Nm2C−2], ε0is permittivity of free space
F = kq1q2
d2Force between two charges
F = q1E Force on charge in field
E = 4πkQ
AUniform electric field between two charged parallel plates, each of area A
−→
E= k q−→
r
r2
−→
rin direction + →-. Electric field of single charge.
W
q=Ed Electric potential
V = IR Ohm’s
P = VI = I2R Power
R = ρl
AResistivity
Rtot = R1+ R2+ ... Resistors in series
1
Rtot =1
R1+1
R2+ ... Resistors in parallel
1.2 Magnetism
~
F=~
Eq +~vq ×~
BLorentz Force Law
~
F=I~
l+×~
BForce on current carrying conductor
B = Φ
AMagnetic induction, Φ=magnetic flux
R = mv
Bq Radius of curvature of moving charge in magnetic field
−→
B=µ0
4π
q−→
v×br
r2Magnetic field of moving charge
1
pf3

Partial preview of the text

Download Electromagnetism Study Notes for GRE Physics and more Study notes Electromagnetism and Electromagnetic Fields Theory in PDF only on Docsity!

1 Electromagnetism

General comments: the GRE is in SI units, so for those who took 8.022, make sure to

pay attention to where the epsilons and mus go. (And thus the slightly different form of

Maxwell’s Equations.)

Also, on one of the practice tests I looked at, they asked about which if Maxwell’s equa-

tions would need to be modified to account for magnetic monopoles.

Work:

W

q 0

has units of volts. Volt = Joules/Coulomb.

1.1 Electricity

k =

1

4 πε 0

[Nm

2 C

− 2 ], ε 0

is permittivity of free space

F = k

q 1

q 2

d

2

Force between two charges

F = q 1 E Force on charge in field

E = 4πk

Q

A

Uniform electric field between two charged parallel plates, each of area A

E = k

q

−→ r

r

2

r in direction + → -. Electric field of single charge.

W

q

= Ed Electric potential

V = IR Ohm’s

P = VI = I

2 R Power

R = ρ

l

A

Resistivity

R

tot

= R

1

+ R

2

  • ... Resistors in series

1

Rtot

1

R 1

1

R 2

  • ... Resistors in parallel

1.2 Magnetism

F =

Eq + ~vq ×

B Lorentz Force Law

F = I

l + ×

B Force on current carrying conductor

B =

Φ

A

Magnetic induction, Φ=magnetic flux

R =

mv

Bq

Radius of curvature of moving charge in magnetic field

B =

μ 0

4 π

q

−→ v ×br

r

2

Magnetic field of moving charge

B · dl = μ 0

I Ampere’s law, use for calculating current

1.3 Capacitors

C =

Q

V

= ε 0

A

d

Capacitance, Q = charge on either plate. [farads]

U

C

1

2

CV

2 Energy of Capacitor

V =

Q

ε 0 A

d

Capacitors in series (or multiple different dielectrics): C =

1 “

1

C 1

”

“

1

C 2

”

Charging: q = (Cε)

1 − e

−t/RC

Discharging: q = (Cε)

e

−t/RC

1.3.1 Undriven

RL Circuit: V R

+ V

L

= RI + L

dI

dt

I(t) = I 0

e

−Rt/L

RC Circuit: V (t) = V 0

e

−t/RC

1.3.2 Driven RLC Circuit

V (t) = V f

︸︷︷︸

forced response

  • Ae

S 1 t

  • Be

S 2 t

natural response

Where S 1 , 2

= −α ±

α

2 − ω

2

0

α =

1

2 RC

, ω 0

1 √

LC

1.4 Maxwell’s Equations

Gauss’s Law

E =

ρ

ε 0

Gauss’s law for magnetism

B = 0

Faraday’s law

∇ ×

E = −

∂

~ B

∂t

Ampere’s Law

∇ ×

B = μ 0

J + μ 0

ε 0

∂

~ E

∂t

NOTE:

J is the total current density.

1.5 Magnetic and electric fields in matter

ε = ε 0 εr for media other than free space, where εr = relative permitivity of the media.

SIMILAR FOR MAGNETS?