Two spherical inflated rubber balloons each have the same amount of charge spread uniformly on their surfaces. If the repelling force is 2.5

Question

Two spherical inflated rubber balloons each have the same amount of charge spread uniformly on their surfaces. If the repelling force is 2.5 N and the distance between the balloon centers is 0.30 m, find how much charge is on each balloon.

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Thành Công 2 months 2021-07-31T22:25:30+00:00 1 Answers 3 views 0

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    2021-07-31T22:27:13+00:00

    Answer:

    5.0\cdot 10^{-6}C

    Explanation:

    The magnitude of the electrostatic force between two charged objects is given by Coulomb’s law:

    F=k\frac{q_1 q_2}{r^2}

    where:

    k=8.99\cdot 10^9 Nm^{-2}C^{-2} is the Coulomb’s constant

    q_1, q_2 are the two charges  on the two objects

    r is the separation between the two charges

    The force is:

    – Repulsive if the two charges have same sign

    – Attractive if the two charges have opposite sign

    In this problem:

    F = 2.5 N is the force between the two balloons

    r = 0.30 m is their separation

    q_1=q_2=q is the charge on each balloon (they have the same charge)

    So, re-arranging the equation, we can find the value of q:

    F=\frac{kq^2}{r^2}\\q=\sqrt{\frac{Fr^2}{k}}=\sqrt{\frac{(2.5)(0.30)^2}{8.99\cdot 10^9}}=5.0\cdot 10^{-6}C

    We are also told that the force between them is repulsive: this means that the charges on the two balloons have  same sign (so, either they are both positive, or both negative).

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