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Math Help - More on Charges

  1. #1
    Super Member Aryth's Avatar
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    More on Charges

    Four particles form a square. The charges are q_1 = q_4 = Q and q_2 = q_3 = q.

    (a) What is \frac Qq if the net electrostatic force on particles 1 and 4 is zero?

    (b) Is there any value of q that makes the net electrostatic force on each of the four particles zero? Explain.
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  2. #2
    Senior Member vincisonfire's Avatar
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    If I understand well how you draw the diagram then
    F_{EQ}=\frac{kQ^2}{(\sqrt{2}c)^2}
     F_{Eq}=\frac{kqQ}{c^2} where c is one side of the square.
    The forces are balanced.
    In the direction of Q  F_{EQ}=2F_{Eq} cos(\frac{\pi}{4})
    I think you should get \frac{Q}{q}= 2\sqrt{2}
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  3. #3
    Super Member Aryth's Avatar
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    If you don't mind me asking, where did the (\sqrt{2}c)^2 come from?

    How did you derive the force equations for Q and q?
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    Senior Member vincisonfire's Avatar
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     \sqrt{2}c is the diagonal of the square.
     F_{EQ}=\frac{kq_1q_2}{r^2} is the electric force equation between two charges.
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  5. #5
    Super Member Aryth's Avatar
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    Ok, I understand the diagonal.

    But I guess I should rephrase my second question.

    Why is it Q^2 for the force on Q, and qQ for the force on q?
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  6. #6
    Senior Member vincisonfire's Avatar
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    The electric force between two particles is proportional to each of the charges and inversely proportional to the square of the distance between them
    <br />
F_{EQ}=\frac{kq_1q_2}{r^2}<br />
    The force of q1 on q2 is the same as q2 on q1. This is action-reaction principle.
    Think of it as gravitation. It is the same. Mass is gravitational charge and "charge" is electric charge. The force of the moon on the earth is the same as the earth on the moon. Effects are different because mass of each is different.
    So the force of Q on Q is <br />
F_{EQ}=\frac{kQ^2}{r^2}<br />
and the force of q on q is <br />
F_{EQ}=\frac{kqQ}{r^2}<br />
Notice that when the two charge are the same sign they tend to repulse each other. The opposite happen when they are of different sign. Here, Q and Q are obviously the same sign. Two charge q have to compensate for one charge Q that is farther.
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