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20 July, 02:20

Identical + 7.67 μC charges are fixed to adjacent corners of a square. What charge (magnitude and algebraic sign) should be fixed to one of the empty corners, so that the total potential at the remaining empty corner is 0 V?

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  1. 20 July, 05:00
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    q₃ = - 13.0935 μC

    Explanation:

    Given

    q₁ = q₂ = + 7.67 μC

    We use the equation

    V = Kq/r

    We can apply it as follows

    V₁ = K*q₁/r₁ = K*q₁ / (√2*L)

    V₂ = K*q₂/r₂ = K*q₂/L

    V₃ = K*q₃/r₃ = K*q₃/L

    Then

    V₁ + V₂ + V₃ = 0

    ⇒ (K*q₁ / (√2*L)) + (K*q₂/L) + (K*q₃/L) = 0

    ⇒ (K/L) * ((q₁/√2) + q₂ + q₃) = 0

    ⇒ (q₁/√2) + q₂ + q₃ = 0

    Since q₁ = q₂

    ⇒ (q₁) ((1/√2) + 1) + q₃ = 0

    ⇒ q₃ = - (q₁) ((1/√2) + 1) = + 7.67 μC * (1.7071)

    ⇒ q₃ = - 13.0935 μC
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