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Physics 1402.001 - Week Eight
The Magnetic Field - Chapter 26
Magnetic Forces on Currents
Magnetic Energy
Hall Effect
Torques on Current Loops
Magnetic Fields
Office Hour
•  My office hour this Tuesday March 7, from
3:30 – 4:30 PM, will be moved to Wednesday
March 8, at the same time.
•  No Office Hours during Spring Break
Magnetic Fields
•  Magnets occur naturally in Nature
Magnetic Fields
•  Magnets occur naturally in Nature
•  Magnets ALWAYS come with BOTH
North and South poles
No Magnetic Single Charges
Force Exerted by Magnetic Fields
Magnetic Fields
•  Magnets occur naturally in Nature
•  Magnets always come with BOTH
North and South poles
•  Unlike Electric Charges, ALL magnets
are Dipoles
•  There are no Magnetic Monopoles
Gauss’ Law for Magnetism
•  Magnetic flux
Φ =
Magnets - How Do They Work?
∫B•n dA
•  There are no net converging or diverging
magnetic field lines
•  Therefore Φ =
∫B•n dA = 0
Force Exerted by Magnetic Fields
•  Moving electric charges create magnetic fields
(More on this in Chapter 27)
•  If moving charges are in presence of external
magnetic field, these two magnetic fields can
interact
•  Net effect is that a charge moving in an external
magnetic field feels an additional Force!
Force Exerted by Magnetic Fields
Force Exerted by Magnetic Fields
Force Exerted by Magnetic Fields
•  F = q v x B
•  Newton = (Coul)(meter/sec)B
•  1 Tesla = Newton/Coul-m/sec
•  1Tesla = Newton/Amp-m = 104 Gauss
Force on Moving Proton
Force on Moving Proton
Force on Moving Proton
Clicker Question No. One
•  Force = q v x B
q = + 1.6 x 10-19 Coul
•  V = 107 m/sec j
|B| = 0.6 G = 6 x 10-5 T
•  B = By j + Bz k = (Bcosθ)j + (-Bsinθ)k
•  (j x j ) = 0
(j x –k) = - i
•  F = (1.6 x 10-19 Coul)(107 m/sec)(-6 x 10-5 T sin70°)i
•  F = - 9 x 10-17 N i
The left diagram shows a positively charged particle
is moving with velocity v in a magnetic field B.
Using the arrows in the right diagram, what is the
direction of the magnetic force on the particle?
Clicker Question No. One
Clicker Question No. Two
The left diagram shows a positively charged particle
is moving with velocity v in a magnetic field B.
Using the arrows in the right diagram, what is the
direction of the magnetic force on the particle?
The left diagram shows a force F on a negatively
charged particle moving a magnetic field B.
Using the arrows in the right diagram, what is the
direction of the velocity of the particle?
Clicker Question No. Two
Force on Current-Carrying Wire
The left diagram shows a force F on a negatively
charged particle moving a magnetic field B.
Using the arrows in the right diagram, what is the
direction of the velocity of the particle?
I = n q Vol/time = n q A L/time = n q A vd
Force on Current-Carrying Wire
Force on Current-Carrying Wire
B = Bx i + By j = Bcos30°i + Bsin30° j
L = 3 mm = 3 x 10-3 m
I = 3.0 A
B = 0.02 T
F = (q vd x B)n A L
I = n q A vd
F = (3 A)(3 x 10-3 m)(0.02T)(sin30°) (i x j)
F=ILxB
dF = I dL x B
F = 9 x 10-5 N k
Physics 1402.001 - Week Eight
Force on Curved Wire
The Magnetic Field - Chapter 26
Magnetic Forces on Currents
Magnetic Energy
Hall Effect
Torques on Current Loops
Force on Curved Wire
Point Charge Moving in Uniform
Magnetic Field
•  F = qvB = ma = mv2/R
•  R = mv/qB
•  (2πR) = v τ = (2πmv/qB)
•  τ = 2πmv/vqB = 2πm/qB
•  ω = 2πf = 2π/τ = qB/m Point Charge Moving in Uniform
Magnetic Field
Clicker Question No. Three
A particle with charge q and mass m is moving
with speed v in the +x direction enters a magnetic
field of strength B pointing in the +y direction.
The work done by the magnetic force on the
particle as it travels one semi-circle is
A. 
B. 
C. 
D. 
E. 
πmqvB
πmv2
πqvB
zero
πmv/qB
Clicker Question No. Three
A particle with charge q and mass m is moving
with speed v in the +x direction enters a magnetic
field of strength B pointing in the +y direction.
The work done by the magnetic force on the
particle as it travels one semi-circle is
A. 
B. 
C. 
D. 
E. 
πmqvB
πmv2
πqvB
zero
πmv/qB
Clicker Question No. Four
Clicker Question No. Four
•  Three particles travel through a region of space where the
magnetic field is out of the page, as shown in the figure. The
electric charge of each of the three particles is, respectively,
• 
• 
• 
• 
• 
A) 1 is neutral, 2 is negative, and 3 is positive.
B) 1 is neutral, 2 is positive, and 3 is negative.
C) 1 is positive, 2 is neutral, and 3 is negative.
D) 1 is positive, 2 is negative, and 3 is neutral.
E) 1 is negative, 2 is neutral, and 3 is positive.
Point Charge Moving in Uniform
Magnetic Field
•  Three particles travel through a region of space where the
magnetic field is out of the page, as shown in the figure. The
electric charge of each of the three particles is, respectively,
• 
• 
• 
• 
• 
A) 1 is neutral, 2 is negative, and 3 is positive.
B) 1 is neutral, 2 is positive, and 3 is negative.
C) 1 is positive, 2 is neutral, and 3 is negative.
D) 1 is positive, 2 is negative, and 3 is neutral.
E) 1 is negative, 2 is neutral, and 3 is positive.
Electron-Positron Pairs
Electron-Positron Pairs
Electron-Positron Pairs
Point Charge Moving in Uniform
Magnetic Field
Magnetic Bottle
Radiation Belts
Aurora Borealis
Clicker Question No. Five
Electrons travel at an initial velocity v0. They pass through a set of
deflection plates, between which there exists an electric field which
deflects them upwards toward point b. In which direction should a
magnetic field be applied so that the electrons land undeflected at a?
Clicker Question No. Five
Electrons travel at an initial velocity v0. They pass through a set of
deflection plates, between which there exists an electric field which
deflects them upwards toward point b. In which direction should a
magnetic field be applied so that the electrons land undeflected at a?
Velocity Selector
Velocity Selector
J.J. Thomson’s Measurement of e/m
•  F = - qE + qv x B
•  If F = 0
•  qE = q v x B = qvB
•  v = E/B
Velocity Selector
Point Charge Moving in Uniform
Magnetic Field
Mass Spectrometer
Mass Spectrometer
q|ΔV| = (1/2) mv2
ω = 2πf = qB/m R = mv/qB
v = qBR/m
v2 = q2B2R2/m2
(1/2) mv2 = (1/2) m (q2B2R2/m2) = q|ΔV|
m/q = (1/2)B2R2/|ΔV|
Al Nier – University of Minnesota
Al Nier – University of Minnesota
Mass Spectrometer
Mass Spectrometer
Torques on Current Loops due to
Magnetic Fields
Torques on Current Loops due to
Magnetic Fields
Use the right hand rule to define
orientation of current loop,
represented by normal vector n
F1 = F2 = I L x B = IaB
Torques on Current Loops due to
Magnetic Fields
F1 and F2 form a “couple” and
“every couple has its moment!”
(But it’s just a lot of torque!)
Torques on Current Loops due to
Magnetic Fields
Calculate torque τ about point P
(so F1 does not contribute to torque)
τ  = F2bsinθ = IaBbsinθ = IB (ab)sinθ
µ = IANn
τ  = µ x Β
Torques on Current Loops due to
Magnetic Fields
Torques on Current Loops due to
Magnetic Fields
Torques on Current Loops due to
Magnetic Fields
Potential Energy of Magnetic Dipole
Spinning Charged Disc
•  dW = - τ dθ = - µB sinθ dθ = - dU
•  U = ∫ µB sinθ dθ = - µB cosθ + Uo
•  If U = 0 when θ = 90°
•  U = - µB cosθ = - µ • B The Hall Effect
The Hall Effect
•  Magnetic force FM = q vd B
•  Balanced by electric force FE = q EH
•  EH = vd B
•  For a width w, VH = EH w = vd B w
•  Hall Voltage VH = vd B w
The Hall Effect
•  Current is deflected by external magnetic field.
The Hall Effect
•  I = n |q | vd A – check units
•  Area A = w t
•  Charges pile up at sides of material, building
up an electric field.
I = n |q | vd w t
•  vd w = I/n |q| t = I/ n e t
•  VH = vd w B = I B/n e t
•  When EH = VH/width the field is strong enough
to prevent one more charge from being
deflected
The Quantum Hall Effect
•  n = I B/VH e t
•  Measure I, B and VH – determine n!