1fields B and using E Devices CYCLOTRON This device works because the angular velocity of a charge moving in a B field is independent of its speed. rrMVFCˆ2−= is provided by rqVBFBˆ−= So MqBrV==ω The cyclotron combines a B and an E -field. In its simplest form it consists of two “DEES” in which there is constant B -field. Say zBBˆ−=. In the gap between them there is an E -field which varies with time at the same angular frequency⎟⎠⎞⎜⎝⎛=MBqω. Suppose at 0 you have a positive charge q which you accelerate with an E -field so it enters the right DEE with a velocity . The xVˆB -field will make it go around a with angular velocity ω. By the time it arrives in the gap E will have reversed as the period of E is the same as ωπ2 so q will get accelerated again. In this way the charge goes round and round within the DEES and gets accelerated each time it crosses the gap. Indeed this device can accelerate charges to quite high speeds. VELOCITY SELECTOR This again uses a combination of E and B and produces a beam of charges with a fixed speed controlled by the ratio BE. 0zBBˆ−= zBBˆ−= E +zBBˆ−= q −2We begin with two parallel plates and establish an E field between them yEEˆ−= Introduce a beam of charges q with a distribution of velocities along the x-axis. Once they enter the E field they will experience a force yqEFEˆ−= -(1) (Recall problem 4-5) which will make them bend downward. Now, we introduce a zBBˆ−= between the plates. It will cause the particles to experience a force yqvEFBˆ= (2) If we choose B correctly, we can make →=+ 0EBFF (3) Hence a charge whose speed satisfies Eq (3) will go between the plates straight through, that is if BEv= the charge goes through. If V is larger charge will hit top plate, if EBFF >BEV < charge will hit bottom plate. MASS SPECTROMETER This device is used to separate beams of isotopes, that is charged particles whose masses re different. Let us say we have a beam of charges q with two masses and . The device is as below. 1M2M3selector vel.21,MMzBBˆ= +q First, use a velocity selector so both masses have velocityyVVˆ=. Next, apply zBBˆ= it will make the charges go on circles of radii qBVMR11= and qBVMR22= thereby separating them. It can also be used to separate two charged beams where particles have the same
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