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Magnetic field ✤ Iron filings may be used to show the pattern of the magnetic field lines. ✤ A compass can be used to trace the field lines. The lines outside the magnet point from the North pole to the South pole. magnetar Magnetic force and magnetic fields Feb 28, 2012 Source of magnetic field ✤ ✤ ✤ Magnetic fields are associated with charge in motion and with elementary charged particle spin. If charge moves in a conductor, for example, a magnetic field is found to circulate around the direction of the moving charge.Details in Chapter 30 Magnetic fields superpose like electric fields. The Earth’s magnetic field ✤ ✤ ✤ The source of the Earth’s magnetic field is likely convection induced electrical currents in the Earth’s core. The direction of the Earth’s magnetic field wanders and reverses. The field shields the Earth from charged particles emitted by the Sun. The north-seeking pole of a compass points to the north geographic pole. ! This would correspond to the Earth’s south magnetic pole. The south-seeking pole points to the south geographic pole. ! This would correspond to the Earth’s north magnetic pole. Pole shifts ✤ https://en.wikipedia.org/wiki/ File:Earth_Magnetic_Field_Declinat ion_from_1590_to_1990.gif During a pole reversal, the field is reduced by a factor of ten. The shielding of the Earth from solar radiation is reduced. Magnetic force ✤ The magnetic field B can be defined by the magnetic force on charged particles. ✤ The force on a charge q with velocity v in a magnetic field B is given by the “cross product” of velocity and field ✤ Ferromagnetism ✤ The magnetic field of a “permanent magnet” is associated with alignment of the spins of charged electrons in atoms. ✤ The electrons behave like a collection of tiny permanent magnets. When these tiny magnets are aligned, not randomly oriented, a net macroscopic magnetization and magnetic field is observed. Strength of magnetic fields FB = q v x B ✤ The magnitude of the magnetic force on a charged particle is FB = |q| v B sin !. ✤ Unit T = Wb m-2 = N C-1 m-1 s. http://solomon.as.utexas.edu/ ~duncan/magnetar.html 1 T = 10,000 gauss Motion in a uniform magnetic field ✤ Consider a particle moving in an external magnetic field with its velocity v perpendicular to the field B. ✤ The force is always directed toward the center of the circular path and does no work so the KE and speed are constant. ✤ The magnetic force causes a centripetal acceleration, changing the direction of the velocity of the particle. ✤ Equate the magnetic and centripetal forces: ✤ ✤ Example ✤ Electrons are observed bending clockwise in a magnetic field perpendicular to the page with radius of curvature r= p/eB. ✤ From the radius and field, the momentum p may be determined. ✤ Given the momentum per unit Does B point into or out of the page? charge created by a known electric field, the quantity q/m may be determined. FB = qvB=ma = mv2/r Solve for r=mv/(qB) = p/(qB) Example Example r ✤ ✤ ✤ ✤ An electron moves in a circle of radius r=1 mm in a magnetic field B= 1 T. An electron moves in a circle of radius r=1 mm in a magnetic field B= 1 T. ✤ What is its speed? What is its speed? ✤ Assume m =9e-31 kg and q=-e = -1.6e-19 C. Assume m =9e-31 kg and q=-e = -1.6e-19 C. ✤ (For v~c, there are relativistic corrections to our formulae.) -V Volts Example (cont) Example (cont) E d 0 Volts v ✤ ✤ What constant electric field strength E would be required to accelerate an electron from rest over a distance d=1 m to a speed c/2 where c is light speed? (Again, for v~c, there are corrections to this result.) ✤ For a constant electric field strength E required to accelerate an electron from rest over a distance d=1 m to a speed c/2 where c is light speed… ✤ If the accelerating field is achieved with equal and opposite charges on two parallel plates separated by d=1 m, a) what is the voltage between the plates and b) what is the surface charge density on the plates?