2/xx/07184 Lecture 22*PHY 184Week 6 Spring 2007Lecture 22Title: The Lorentz Force = q v x B

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2/xx/07184 Lecture 22*ReviewThe force that a magnetic field exerts on a charge moving with velocity v is given by

The direction is sideways (RH rule).The magnitude of the force

If the charge moves perpendicular to the magnetic field then

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2/xx/07184 Lecture 22*Review (2)The unit of magnetic field strength the tesla (T)

Another unit of magnetic field strength that is often used but is not an SI unit is the gauss (G)

Typically the Earths magnetic field is about 0.5 G at the surface.

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2/xx/07184 Lecture 22*Example: Cathode Ray TubeConsider the cathode-ray tube used for lecture demonstrations.In this tube electrons form an electron beam when accelerated horizontally by a voltage of 136 V in an electron gun.The mass of an electron is 9.109410-31 kg while the elementary charge is 1.602210-19 C.(a) Calculate the velocity of the electrons in the beam after leaving the electron gun.

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2/xx/07184 Lecture 22*Cathode Ray Tube (2)(b) If the tube is placed in a uniform magnetic field, in what direction is the electron beam deflected?

(c) Calculate the magnitude of acceleration of an electron if the field strength is 3.6510-4T.downward

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2/xx/07184 Lecture 22*Particle Orbits in a Uniform BTie a string to a rock and twirl it at constant speed in a circle over your head.The tension of the string provides the centripetal force that keeps the rock moving in a circle.The tension on the string always points to the center of the circle and creates a centripetal acceleration.

A particle with charge q and mass m moves with velocity v perpendicular to a uniform magnetic field B.The particle will move in a circle with a constant speed v and the magnetic force F = qvB will keep the particle moving in a circle.

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2/xx/07184 Lecture 22*Particle Orbits in Uniform B (2)Recall centripetal acceleration

Newton;s second law

So, for charged particle q in circular motion in magnetic field Ba = v2/rF = m a

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2/xx/07184 Lecture 22*Example - Moving ElectronsIn this photo, an electron beam is initially accelerated by an electric field.Then the electrons move in a circle perpendicular to the constant magnetic field created by a pair of Helmholtz coils.Is the magnetic field into the page or out of the page?(Remember that the magnetic force on an electron is opposite that on a proton.)The magnetic field is out of the page.

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2/xx/07184 Lecture 22*Clicker QuestionThe figure shows the circular paths of two particles that travel at the same speed in a uniform magnetic field (directed into the page). One particle is a proton and the other is an electron. Which particle follows the smaller circle? A) the electron B) the proton C) Both, proton and electron travel along on the same circle

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2/xx/07184 Lecture 22*Clicker QuestionThe figure shows the circular paths of two particles that travel at the same speed in a uniform magnetic field (directed into the page). One particle is a proton and the other is an electron. Which particle follows the smaller circle? A) the electron for same speeds, r is proportional to m

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2/xx/07184 Lecture 22*Example: Mass Spectrometer (1)Suppose that B=80mT, V=1000V. A charged ion (1.6022 10-19C) enters the chamber and strikes the detector at a distance x=1.6254m. What is the mass of the ion?Key Idea: The uniform magnetic field forces the ion on a circular path and the ions mass can be related to the radius of the circular trajectory.

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2/xx/07184 Lecture 22*Example: Mass Spectrometer (2)Suppose that B=80mT, V=1000V. A charged ion (1.6022 10-19C) enters the chamber and strikes the detector at a distance x=1.6254m. What is the mass of the ion?From the figure: r=0.5xAlso need the velocity v after the ion is accelerated by the potential difference VNow solve for m3.4x10-25 kg

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2/xx/07184 Lecture 22*Example: The Time Projection ChamberIn high-energy nuclear physics, new forms of matter are studied by colliding gold nuclei at very high energiesIn particle physics, new elementary particles are created and studied by colliding protons and anti-protons at the highest energiesIn these collisions, many particles are created that stream away from the interaction point at high speedsA simple particle detector is not sufficient to measure and identify these particlesA device that can help physicists study these collisions is the time projection chamber (TPC)

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2/xx/07184 Lecture 22*Example: The Time Projection Chamber (2)The STAR TPC consists of a large cylinder filled with a carefully chosen gas (90% argon, 10% methane) that allows free electrons to drift without recombiningAs created charged particles pass through the gas, the particles ionize the atoms of the gas, releasing free electronsAn electric field is applied between the center of the TPC and the caps of the cylinder that exerts an electric force on these freed electrons, making them drift to the end-caps of the TPC, where they are recorded electronicallyUsing the drift time and the recording positions, the computer software reconstructs the trajectories that the produced particles took through the TPC

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2/xx/07184 Lecture 22*Example: The Time Projection Chamber (3)The TPC sits inside a giant solenoid magnet shown to the right with the magnetic field pointing along the beam directionThe produced charged particles have a component of their velocity that is perpendicular to the magnetic field and thus have circular trajectories when viewed end-onFrom the radius of curvature one can extract the particle momentum

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2/xx/07184 Lecture 22*Events in the TPCHere are two events in the STAR TPC at Brookhaven National LabMagnetic field is directed into the screenLets analyze this track

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2/xx/07184 Lecture 22*Example - Momentum of a TrackCalculate the momentum of this track

r = 2.3 m

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2/xx/07184 Lecture 22*Orbits in a Constant Magnetic FieldIf a particle performs a complete circular orbit inside a constant magnetic field, then the period of revolution of the particle is just the circumference of the circle divided by the speed

From the period we can get the frequency and angular frequency

The frequency of the rotation is independent of the speed of the particle.Isochronous orbits.Basis for the cyclotron.

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2/xx/07184 Lecture 22*CyclotronsA cyclotron is a particle acceleratorThe D-shaped pieces (descriptively called dees) have alternating electric potentials applied to them such that a positively charged particle always sees a negatively charged dee ahead when it emerges from under the previous dee, which is now positively chargedThe resulting electric field accelerates the particleBecause the cyclotron sits in a strong magnetic field, the trajectory is curvedThe radius of the trajectory is proportional to the momentum, so the accelerated particle spirals outward

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2/xx/07184 Lecture 22*Example: Deuteron in CyclotronSuppose a cyclotron is operated at frequency f=12 MHz and has a dee radius of R=53cm. What is the magnitude of the magnetic field needed for deuterons to be accelerated in the cyclotron (m=3.34 10-27kg)?Key Idea: For a given frequency f, the magnetic field strength, B, required to accelerate the particle depends on the ratio m/q (or mass to charge):

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2/xx/07184 Lecture 22*Special ClickerSuppose a cyclotron is operated at frequency f=12 MHz and has a dee radius of R=53cm. What is the kinetic energy of the deuterons in this cyclotron when they travel on a circular trajectory with radius R (m=3.34 10-27kg, B=1.57 T)? A) 0.9 10-14 J B) 8.47 10-13 J C) 2.7 10-12 J D) 3.74 10-13 J

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2/xx/07184 Lecture 22*K500 Superconducting CyclotronMovie from Nova program The Nucleus Factory

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************Blackboard calculation**********