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26 February, 16:47

An electron in a vacuum is first accelerated by a voltage of 79900 V and then enters a region in which there is a uniform magnetic field of 0.364 T at right angles to the direction of the electron's motion. What is the force on the electron due to the magnetic field?

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  1. 26 February, 20:29
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    9.762 * 10⁻¹² N

    Explanation:

    Given:

    Voltage, V = 79900 Volts

    Magnetic field, B = 0.364 T

    Now,

    The energy (E) due to the applied potential difference,

    E = eV

    where,

    e is the charge of the electron = 1.6 * 10⁻¹⁹ C

    thus,

    E = 1.6 * 10⁻¹⁹ * 79900 J

    also,

    kinetic energy due to the applied potential

    K. E = (1/2) mv²

    where, m is the mass of the electron

    v is the velocity of the electron

    also

    E = K. E

    thus we have

    1.6 * 10⁻¹⁹ * 79900 J = (1/2) * 9.1 * 10⁻³¹ * v²

    or

    v = 1.676 * 10⁸ m/s

    therefore,

    The force in the electron, F = evB

    or

    F = 1.6 * 10⁻¹⁹ * 1.676 * 10⁸ * 0.364

    or

    F = 9.762 * 10⁻¹² N
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