B+fields+_+forces-2
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Transcript of B+fields+_+forces-2
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MagneticFields
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Magnetism
Interactions between magnets described in terms of poles.
“magnetic charges” – opposites attract
Interactions due to magnetic field .
Compass needles – align w/
Direction of force – direction of force on a N pole
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Magnetic Field
Similar to :
• Vector field
• Two “charges” (poles)
Except…
No magnetic monopoles
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Forces on Magnetic Charges
From empirical studies:
• toplane
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Cross Products
Review Cross Products (Ch. 1)
CW: (i.e., )
CCW: (i.e., )
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Forces on Magnetic Charges (cont.)
Direction (RHR):
• Point fingers of right hand in direction of
• Thumb: to fingers
• Curl fingers toward .
• Thumb points in direction of (on )
• : is opposite direction
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Example
Determine the missing directions.
Direction of…
A
B
C
D particle 0
E C
F
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Forces on Magnetic Charges (cont.)
Magnitude of the force
SI units: Teslas,
Another unit: Gauss,
In and :
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Example
A charged particle travels with a speed of in a region where the magnetic field is in the direction and has a magnitude of . Determine the magnitude and direction of the magnetic force if the particle is (a) an electron traveling in the direction; (b) a proton traveling in the direction; (c) an particle traveling in the direction; and (d) an ion traveling in the direction.
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Example
An electron travels in a straight line in the direction with a velocity of . There is both an electric and a magnetic field in this region. (a) If the magnetic field points in the direction and has a magnitude of , what is the magnitude and direction of the electric field? (b) A electric field points in the direction. What is the magnitude and direction of the magnetic field in this situation? The gravitational force on the electron can be ignored.
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Magnetic Field Lines
Field lines can never intersect.
Field lines form closed loops (have no starting/ ending point).
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Magnetic Field Lines (cont.)
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Magnetic Flux
Units: , webers
Gauss’ Law for Magnetism:
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Motion of Charged Particles in
does no work on a moving charge.
cannot change , only direction.
If , not :
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Motion of Charged Particles in
does no work on a moving charge.
cannot change , only direction.
If , not :
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Application: Velocity Selector
Charge moving in both and
with specific :
No deflection of particle (straight line).
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Example
A negatively-charged chlorine isotope is accelerated through a potential difference of . It then enters a region of crossed electric and magnetic fields. (a) Which plate, or , has the higher potential? After exiting plate , the isotope then travels undeflected with speed through a region of crossed, uniform electric and magnetic fields. (b) Determine the charge-to-mass ratio of the isotope. (c) If , , , and , determine the mass of the isotope.
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Application:
J. J. Thomson (for )
Accelerate through . Enter region w/ both and .
Conservation of energy + velocity selector.
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Example
A charged isotope (charge , mass ) travels through a velocity selector undeflected with speed . It then enters a region where there is a magnetic field which has a magnitude of as shown in the figure. Determine, , the distance from where the isotope enters the second magnetic field the mass strikes the detector.
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Application: Mass Spectrometer
Uses velocity selector to isolate isotopes
Radius of path (i.e., how far from opening strike detector)
All other values are measurable.
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Magnetic Force on a Conductor
Conductor (length ) carries current in
Direction: same RHR for charges
: vector of length , in direction of
Magnitude:
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Example
A loop of current is pulled into a region where there is a magnetic field as shown in the figure. If the length of the sides of the loop are , the current through the loop is and the magnetic field has a magnitude of , what is the net force on the loop?
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Force on a Current Loop
Assume uniform .
Axis of rotation = axis.
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Force & Torque on a Current Loop
due to , along axis.
due to due to
due to
Direction of : RHR (fingers = , thumb = )
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Magnetic (Dipole) Moment
Direction of : RHR (fingers = , thumb = )
Points from S N
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Potential Energy (& Coils)
Work to move through angle (align , ):
For stacked loops (i.e., a coil):
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Example
The loop in the picture has a radius of and carries a current in the direction shown. The loop is free to rotate about an axis perpendicular to the page and is tilted so that a line perpendicular to the face of the loop makes an angle of with a magnetic field to the right. (a) Will this loop rotate clockwise or counterclockwise? (b) What is the magnitude of the torque on the loop?
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Non-uniform
Axis of coil is parallel to page.
Looking toward magnet from right, is CW.
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How to Magnetize An Object w/o Really Tryingor
Why Magnets “Stick” to the Fridge
S
N
N
S