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Unformatted text preview: Physics 2102 Aurora Borealis Jonathan Dowling Physics 2102
L ectu re 1 4 C h 2 8 : M a g n e t ic F o r c e s o n C u r r e n t W ir e s
Star Quake on a “I’ll be back…. Magnetar! C r o s s e d F ie ld s E v s . B
q v B E y L FE=qE
FB=vqBFE FE=ma => y=qEL2/(2mv2)
FB=FE => y=0 => v=E/B M a g n e t ic f o r c e o n a w ir e . L L
q = it = i
F = q vd ! B r
iL r r r
F = q !B =iL!B
F =iL!B Note: If wire is not straight,
compute force on differential
elements and integrate: r
dF = i dL ! B E x a m p le
Wire with current i.
Magnetic field out of page.
What is net force on wire?
F1 = F3 = iLB
dF = iBdL = iBRd! By symmetry, F2 will only
have a vertical component,
" " 0 0 F2 = ! sin(# )dF =iBR ! sin(# )d# = 2iBR Ftotal = F1 + F2 + F3 = iLB + 2iRB + iLB = 2iB ( L + R )
Notice that the force is the same as that for a straight wire,
and this would be true no
matter what the shape of
the central segment!. Example 4: The Rail Gun
• Conducting projectile of length 2cm,
mass 10g carries constant current
100A between two rails.
• Magnetic field B = 100T points
• Assuming the projectile starts from
rest at t = 0, what is its speed after a
time t = 1s? rails
B L I projectile • Force on projectile: F= ILB
(from F = iL x B)
• Acceleration: a = iLB/m
(from F = ma)
• v(t) = iLBt/m
(from v = v0 + at)
= (100A)(0.02m)(100T)(1s)/(0.01kg) = 2000m/s
= 4,473mph = MACH 8! Principle behind electric motors. T o rq u e o n a C u rren t L o o p :
Rectangular coil: A=ab, current = i Net force on current loop = 0
But: Net torque is NOT zero! F1 = F3 = iaB F" = F1 sin(! )
Torque = " = F#b = iabB sin(! )
For a coil with N turns,
τ = N I A B sinθ,
where A is the area of coil Magnetic Dipole Moment
We just showed: τ = NiABsinθ
N = number of turns in coil
A=area of coil.
Define: magnetic dipole moment µ r
µ = ( NiA)n r
µ, n Right hand rule:
curl fingers in
direction of current;
thumb points along µ rrr
" = µ!B As in the case of electric dipoles, magnetic dipoles tend to align
with the magnetic field. Electric vs. Magnetic Dipoles
µ = ( NiA)n +Q
" = p! E rrr
" = µ!B ...
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This note was uploaded on 11/18/2011 for the course PHYSICS 2102 taught by Professor Dowling during the Fall '10 term at LSU.
- Fall '10