Magnetic force on a moving charge
Magnetic force on a current-carrying wire
Magnetic field created by a moving charge
Biot-Savart field created by a wire carrying a current
Biot-Savart field created by a straight wire
Force between parallel wires
Ampere’s law
Field inside a coil: Field inside a toroidal solenoid
Faraday’s Law
Inductance . For a toroidal solenoid:
Magnetic energy
2
0
ˆ
4
r
rvq
B×
=
v
v
π
µ
BvqF
r
v
r
×=
BI
L
F
r
r
r
×=
2
0
ˆ
4
r
rldI
B×
=
r
v
π
µ
r
I
B
π
µ
2
0
=
v
L
r
II
F
π
µ
2
'
0
=
thru
Loop
IldB
0
µ
∫
=⋅
r
r
dt
d
ldE
B
Loop
Φ
−=⋅=
∫
r
r
ε
where
I
L
dt
dI
L
B
Φ
=−=
ε
0
2
2
2
and
2
1
µ
B
uLIU==
I
L
N
nIB
00
µµ
==
r
NI
B
π
µ
2
0
=
r
AN
L
π
µ
2
2
0
=
