Two charges are fixed in place on the x-axis as shown. The charge at x = 0 is ne

Question

Two charges are fixed in place on the x-axis as shown. The charge at x = 0 is negative and has magnitude q = 2 ?Coulombs (1 ?Coulomb = 10-6 Coulombs). The charge at x = d, (d = +12 cm), is positive and has magnitude Q = 4 ?Coulombs. Find a point x = xo along the x-axis at which the electric field is zero. To solve this problem you will need to solve a quadratic equation. It will also help if you draw a representation of the field contributed by each charge in the three different regions. This will then guide you to choose the correct solution to the quadratic equation since it will offer you two possible answers.

xo =

Explanation / Answer

q1 = -2 * 10 ^ -3 'C
q2 = 4 * 10 ^ -3 'C
k = 9 * 10 ^ 9
12 centimeters = 0.12 meters

E1 = k * q1 / (xo) ^ 2
E2 = k * q2 / (xo+0.12) ^ 2

solving for x:
xo= 0.12 / (Sqr(q2 / |q1|) - 1)

xo =0.2897 m "Left of origin"
xo = 28.97 cm

check:
E1 = -214466094 N/C
E2 = 214466094 N/C
?E=0

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