lecture14

# Lecture14 - 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

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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 vd r rr F = q vd ! B r r iL r r r F = q !B =iL!B q r rr F =iL!B Note: If wire is not straight, compute force on differential elements and integrate: r rr 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 L R R L 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 outward. • 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 ˆ µ = ( NiA)n r ˆ 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 r ˆ µ = ( NiA)n +Q p=Qa -Q QE θ QE rrr " = 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.

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