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

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 ...
View Full Document

This note was uploaded on 11/18/2011 for the course PHYSICS 2102 taught by Professor Dowling during the Fall '10 term at LSU.

Ask a homework question - tutors are online