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30 April, 02:34

An electron moving parallel to a uniform electric field increases its speed from 2.0 * * 1077 m/sm/s to 4.0 * * 1077 m/sm/s over a distance of 1.3 cmcm.

What is the electric field strength?

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  1. 30 April, 03:16
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    262 kN/C

    Explanation:

    If the electrons is moving parallel, thus it has a retiline movement, and because the velocity is varing, it's a retiline variated movement. Thus, the acceleration can be calculated by:

    v² = v0² + 2aΔS

    Where v0 is the initial velocity (2.0x10⁷ m/s), v is the final velocity (4.0x10⁷ m/s), and ΔS is the distance (1.3 cm = 0.013 m), so:

    (4.0x10⁷) ² = (2.0x10⁷) ² + 2*a*0.013

    16x10¹⁴ = 4x10¹⁴ + 0.026a

    0.026a = 12x10¹⁴

    a = 4.61x10¹⁶ m/s²

    The electric force due to the electric field (E) is:

    F = Eq

    Where q is the charge of the electron (-1.602x10⁻¹⁹C). By Newton's second law:

    F = m*a

    Where m is the mass, so:

    E*q = m*a

    The mass of one electrons is 9.1x10⁻³¹ kg, thus, the module of electric field strenght (without the minus signal of the electron charge) is:

    E * (1.602x10⁻¹⁹) = 9.1x10⁻³¹ * 4.61x10¹⁶

    E = 261,866.42 N/C

    E = 262 kN/C
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