M asked in Science & MathematicsPhysics · 3 months ago

I tried to solve this problem (Q (a)) but i couldnt find the value of q. any idea how to solve it?

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  • 3 months ago
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    Forces on q₁ are as follows

    F₂ (due to q₂) = kq₁q₂/a²

    F₂x = kq₁q₂/a², F₂y = 0

    F₃ (due to q₃) = kq₁q₃/a²

    F₃x = 0, F₃y = kq₁q₃/a²

    F₄ (due to q₄) = kq₁q₄/(√2a)² = kq₁q₄/2a²

    F₄x = F₄cos45 = (1/√2)kq₁q₄/2a²

    F₄y = F₄sin45 = (1/√2)kq₁q₄/2a²

    using q₂ = q₃ = q and q₄ = q₁

    1/(2√2) = √2/4

    F₂x = kq₁q/a², F₂y = 0

    F₃x = 0, F₃y = kq₁q/a²

    F₄x = F₄cos45 = (√2)kq₁²/(4a²)

    F₄y = F₄sin45 = (√2)kq₁²/(4a²)

    add up the x and y components and set equal to zero

    Fx = (kq₁q/a²) + (√2)kq₁²/(4a²) = 0

    Fy = (kq₁q/a²) + (√2)kq₁²/(4a²) = 0

    so one of the forces is opposed to the other, eg, q₁ is negative

    (kq₁q/a²) = (√2)kq₁²/(4a²)

    q = (√2)q₁/(4) = 0.354q₁

    Coulomb's law, force of attraction/repulsion

    F = kQ₁Q₂/r²

    Q₁ and Q₂ are the charges in coulombs

    F is force in newtons

    r is separation in meters

    k = 8.99e9 Nm²/C²

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