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7 July, 18:17

Find the two possible values x3, r and x3,ℓ for the position of charge 3.

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  1. 7 July, 22:12
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    Given:

    q1 = q

    q2 = 4q

    q3 = q

    d = 2.00 cm

    xq1 = 0 cm

    xq2 = 2.00 cm

    q = 2.00 nC

    Let us determine the forces:

    F 1on3 = K ⋅ |q1 | ⋅ |q 3| / r2 = K ⋅ |q| ⋅ |q| / (d 1-3) 2 = K ⋅ q 2 / (d1-3) 2

    F 2on3 = K ⋅ |q2 | ⋅ |q 3| / r2 = K ⋅ |4q| ⋅ |q| / (d 3-2) 2 = K ⋅ 4q 2 / (d3-2) 2

    We're able to solve for the variables in both cases since the forces are supposed to equal each other in each case.

    F 1on3 = F2on3

    K ⋅ q 2 / x 2 = K ⋅ 4q2 / (2.00 cm - x) 2

    1/x2 = 4 / [4.00 cm2 - (4.00 cm⋅x) + x 2]

    [4.00 cm2 - (4.00 cm ⋅ x) + x 2] / x2 = 4

    4.00 cm 2 / x2 - (4.00 cm ⋅ x) / x 2 + x 2 / x2 - 4 = 0

    4.00 cm 2 / x2 - (4.00 cm) / x + 1 - 4 = 0

    4.00 cm 2 / x2 - (4.00 cm) / x - 3 = 0

    3 = 4.00 cm 2 / x2 - (4.00 cm) / x

    3x 2 = 4.00 cm - 4.00 cm ⋅ x

    3x2 + 4.00 cm ⋅ x - 4.00 cm = 0

    After we plug that into the quadratic equation, we get:

    x = - 2 & x = 2/3

    x3, r, x3,ℓ = 0.667,-2.00 cm, cm
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