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27 December, 03:44

Hans Langseth's beard measured 5.33 m in 1927. Consider two charges, q1 = 2.42 nC and an unspecified charge, q2, are separated 5.33m. A third charge of 1.0 nC is placed 1.9 m away from q1. If the net electric force on this third charge is zero, what is q2? (Give your answer in nC

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  1. 27 December, 03:52
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    -7.89 * 10^ (-9) C

    Explanation:

    Parameters given:

    q1 = 2.42 nC = 2.42 * 10^ (-9) C

    Distance between q1 and q2 = 5.33 m

    q3 = 1.0 nC = 1 * 10^ (-9) C

    Distance between q1 and q3 = 1.9 m

    Distance between q2 and q3 = 5.33 - 1.9 = 3.43 m

    The net force acting on q3 is:

    F = F (q1, q3) + F (q2, q3)

    F = (k*q1*q3) / 1.9² + (k*q2*q3) / 3.43²

    F = (9 * 10^ (9) * 2.42 * 10^ (-9) * 1 * 10^ (-9)) / 3.61 + (9 * 10^ (9) * q2 * 1 * 10^ (-9)) / 11.7649

    F = 6.033 * 10^ (-9) + 0.765*q2

    If the net force is zero:

    0 = 6.033 * 10^ (-9) + 0.765*q2

    -0.765*q2 = 6.033 * 10^ (-9)

    => q2 = - [6.033 * 10^ (-9) ]/0.765

    q2 = - 7.89 * 10^ (-9) C
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