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23 July, 13:54

Part A By what distance do two objects carrying 1.0 C of charge each have to be separated before the electric force exerted on each object is 4.0 N? Express your answer with the appropriate units.

Part B How much charge should be placed on each of two small objects separated by 1.0 m so that the electric force exerted on each is 4.0 N? Express your answer with the appropriate units.

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  1. 23 July, 17:47
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    Part A: 4.74*10⁴ m

    Part B: 0.000211 C

    Explanation:

    Part A:

    From coulombs law,

    F = kq²/r² ... Equation 1

    Note: The two object are carrying equal charges.

    Where F = Electric force, q = charge, r = distance of separation, k = proportionality constant

    Given: F = 4.0 N, q = 1.0 C,

    Constant: k = 1/4πe₀ = 9*10⁹ Nm²/C²

    Substituting these values into equation 1,

    4 = 9*10⁹ (1²) / r²

    r² = (9*10⁹) / 4

    r² = 2.25*10⁹

    r = √ (2.25*10⁹)

    r = 4.74*10⁴ m.

    Part 2:

    F = kq²/r²

    Making q the subject of the equation

    q = √ (Fr²/k) ... Equation 2

    Where: F = 4.0 N, r = 1.0 m, k = 9*10⁹ Nm²/c²

    Substituting these values into equation 2

    q = √ (4*1² / (9*10⁹)

    q = 2.11/10⁴

    q = 0.000211 C.
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