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Magnetic force on a moving charge
r
v r
F = qv × B
Magnetic force on a current-carrying wire
r
r r
F = LI × B
v µ0 qvv × rˆ
Magnetic field created by a moving charge B =
4π r 2
r
v µ0 I dl × rˆ
B
=
Biot-Savart field created by a wire carrying a current
4π r 2
v µ0 I
Biot-Savart field created by a straight wire B =
2πr
Force between parallel wires
F=
µ0 I ' I
L
2πr
r r
∫ B ⋅ dl =µ0 I thru
Ampere’s law
Loop
Field inside a coil:
Faraday’s Law
Inductance
B = µ0nI = µ0
Field inside a toroidal solenoid
B=
µ0 NI
2πr
r r
dΦ B
ε = ∫ E ⋅ dl = −
dt
Loop
ε = −L
Magnetic energy
N
I
L
dI
Φ
where L = B
dt
I
1 2
B2
U = LI and u =
2
2 µ0
. For a toroidal solenoid:
µ0 N 2 A
L=
2πr
Units and constants:
Electricity:
ε 0 = 8.854 × 10−12 C2 /N.m2 and
1
4πε 0
= 9.0 × 109 N.m2 / C2
e = 1.602 × 10−19 C
[Charge]=Coulomb=C
[Electric Force]=Newton=N
[Electric Field]=[Force]/[Charge]=N/C=[Voltage]/[distance]=Volt/meter= V/m
[Energy]=Newton.meter=Joule=J
[Voltage]=[Energy]/[Charge]=J/C=Volt=V
[Capacitance] = [Charge]/[Voltage]=Coulomb/Volt=C/V=Farad=F
[Current] = [Charge]/[time]=Coulomb/sec.=C/s=Amp=A
[Resistance] = [Voltage]/[Current]=Volt/Amp= Ohm=Ω
Magnetism:
µ0 = 4π × 10−7 Tm/A and
µ0
= 10−7 T.m / A
4π
[Magnetic Field]=[Newton/Ampere.meter] =N/Am=Tesla=T
[Inductance]= [L] = [Tesla meter2]/[Amperes] = [Henry]=H