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28 December, 05:40

A tiny sphere of mass 7.70 mg and charge - 2.80 nC is initially at a distance of 1.64 μm from a fixed charge of + 8.69 NC.

(a) If the 7.70-mg sphere is released from rest, find its kinetic energy when it is 0.500 μm from the fixed charge.

(b) If the 7.70-mg sphere is released from rest, find its speed when it is 0.500 μm from the fixed charge.

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  1. 28 December, 06:08
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    We shall apply conservation of energy in an electrical field to solve the problem.

    potential energy initial of sphere = 9 x 10⁹ x Q q / d, Q and q are two given charges at d distance.

    Q = 8.69 x 10⁻⁹C, q = - 2.8 x 10⁻⁹ C, d = 1.64 x 10⁻⁶ m

    potential energy V₁ at distance 1.64 x 10⁻⁶

    = - 2.8 x 8.69 x 10⁻¹⁸x 9 x 10⁹ / 1.64 x 10⁻⁶

    = - 133.53 x 10⁻³ J

    potential energy V₂ at distance 0.5 x 10⁻⁶

    = - 2.8 x 8.69 x 10⁻¹⁸x 9 x 10⁹ /.5 x 10⁻⁶

    = - 437.97 x 10⁻³ J

    Decrease in potential energy = 304.44 x 10⁻³ J.

    This will result in increase in kinetic energy

    kinetic energy at. 5 m = 304 x 10⁻³ J

    b) 1 / 2 m v² = kinetic energy, m is mass and v is velocity

    1 / 2 m v² = 304 x 10⁻³

    v² = 2 x 304 x 10⁻³ / 7.7 x 10⁻³

    = 79

    v = 8.9 m / s
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