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22 January, 23:54

Problem 7: In a mass spectrometer, a specific velocity can be selected from a distribution by injecting charged particles between a set of plates with a constant electric field between them and a magnetic field across them (perpendicular to the direction of particle travel). If the fields are tuned exactly right, only particles of a specific velocity will pass through this region undeflected. Consider such a velocity selector in a mass spectrometer with a 0.095 T magnetic field.

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  1. 23 January, 00:12
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    Complete question

    In a mass spectrometer, a specific velocity can be selected from a distribution by injecting charged particles between a set of plates with a constant electric field between them and a magnetic field across them (perpendicular to the direction of particle travel). If the fields are tuned exactly right, only particles of a specific velocity will pass through this region undeflected. Consider such a velocity selector in a mass spectrometer with a 0.095 T magnetic field.

    a. What electric field strength, in volts per mater, is needed to select a speed of 4.2 x 10^6 m/s?

    b. What is the voltage, in kilovolts, between the plates if they are separated by 0.95 cm?

    Explanation:

    Given that,

    magnetic field B = 0.095T

    Speed of particle v = 4.2 * 10^6m/s

    Separation between plate d = 0.95cm

    d = 0.95/100 = 0.0095m

    a. Using the mass spectrometer velocity selector relationship between the electric field and magnetic field.

    v = E/B

    Where

    v is the speed selector

    B is magnetic field

    E is electric field

    Therefore, E = vB

    E = 4.2 * 10^6 * 0.095

    E = 0.399 * 10^6

    E = 3.99 * 10^5 V/m

    b. Voltage?

    The relationship between electric field and potential difference between the two plates is given as

    V = Ed

    V = 3.99 * 10^5 * 0.0095

    V = 3790.5 V

    To kV, 1kV = 1000V

    Then, V = 3.7905kV

    V ≈ 3.791 kV
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