Unit 4 Day 3 – Magnetic Dipole
Moment & Applications
• Magnetic Torque
• Magnetic Dipole Moment
• Potential Energy of a Magnetic
Dipole
• Magnetic Moment of a Hydrogen Atom
• Applications of magnetic Dipole Moment
Magnetic Torque
• When a loop of wire carrying a current
is placed in a uniform magnetic field,
the magnetic force will produce a torque
on the loop, causing it to rotate
• This is the principle behind motors,
analog voltmeters, and etc.
Magnetic Torque
• The torque on the dipole is:
 net  Fnet  d   Il  B   d 
b
b
  CW  IaB    IaB  
2
2
 IabB  IAB
where A  ab area of the coil ) 
• If the coil consists of N loops
the current increases by N·I
   NIAB
Magnetic Torque
• If the coil makes an angle θ
with the magnetic field, the
magnetic force remains the
same but the lever arm is
reduced from ½b to ½bsinθ
• Torque is always in the direction
the net force
of
   NIAB sin 
• Although this formula was derived for a rectangular coil,
it is valid for any shape of flat coil
Magnetic Dipole Moment
• The quantity NIA in the torque formula is called the
“magnetic dipole moment”
  NI A
Where the direction of A is in the direction of μ
• Therefore, in vector form, torque is expressed as:
  NI A  B
or
 uB
Magnetic Dipole Potential Energy
• Remember the torque on an electric dipole:
  p  E where p is the electric dipole moment
• The electric potential energy of the electric
dipole is:
U  p E
• Hence, the magnetic potential energy of a
magnetic dipole is:
U    B
Magnetic Moment of a Hydrogen Atom
vt
• The hydrogen atom consists
of a (-) charged electron
orbiting a (+) charged proton
FC
• The Coulombic force of
attraction is the equivalent
of the centripetal force keeping
the electron in orbit
Fcentripetal  FCoulombic
me vt2
e2

r
40 r 2
solving for vt
vt 
e2
 2.19  106 ms
40 me r
  12 evt r  9.27  10 24
J
T
Applications of Magnetic Dipole
Moment
Electric Motors
Loud Speaker
Voltmeter (Galvanometer)