A beam of electrons is accelerated through a potential difference of 7.0 kV before entering a velocity selector. If the B-field of the veloc

Question

A beam of electrons is accelerated through a potential difference of 7.0 kV before entering a velocity selector. If the B-field of the velocity selector is perpendicular to the velocity and has a value of 0.04 T, what value of the E-field is required (in the magnetic field region) if the particles are to be undeflected?

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Delwyn 2 weeks 2021-08-31T12:11:51+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-08-31T12:13:07+00:00

    Given Information:  

    Potential difference = V = 7 kV  

    Magnetic field = B = 0.04 T  

    Required Information:  

    Electric Field = E = ?

    Answer:

    Electric Field = 1.98×10⁶ V/m

    Step-by-step explanation:  

    The required Electric field can be found using

    E = vB

    Where v is the velocity of electron beam and B is the magnetic field

    But first we need to calculate the velocity

    V = E/q

    E = Vq

    Where V is the potential difference and q is the charge 1.60×10⁻¹⁹ C

    E = 7×10³*1.60×10⁻¹⁹

    E = 11.2×10⁻¹⁶ J

    As we know

    E = ½mv²

    Where m is the mass of electron 9.11×10⁻³¹ kg

    v = √2E/m

    v = √2*11.2×10⁻¹⁶/9.11×10⁻³¹

    v = 4.958×10⁷ m/s

    Finally we can now calculate the Electric field

    E = vB

    E = 4.958×10⁷*0.04

    E = 1.98×10⁶ V/m

    Therefore, an electric field of 1.98×10⁶ V/m is required if the particles are to be undeflected.

    0
    2021-08-31T12:13:15+00:00

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