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Two small spheres, each of mass 3.00 g , are suspended by light strings 10.0 cm in length (see figure). A uniform electric field is applied in the x direction. The spheres have charges equal to -6.0 * 10 ^ -8 C and 6.0 * 10 ^ -8 C. Determine the electric field that enables the spheres to be in equilibrium at an angle of theta = 10 degrees. [diagram]

Round your answer to three significant figures. Take the Coulomb constant to be 8.99 * 10 ^ 9 and the acceleration of gravity to be -9.8 m/s/s

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Positive charge = Q1, negative charge = Q2

Consider all forces acting on Q1

In the y-direction:

force of gravity, 9.8 m/s/s * 0.003 kg = 0.0294 N

Y-component of tension, T * cos10

In equilibrium, forces are equal, T * cos10 = 0.0294 N, so 0.0294 N / cos 10 = T

Magnitude of tension = 0.02985 N

In the x-direction:

force of Q2 on Q1, given by k * ( |Q1| * |Q2| ) / r ^ 2

Where r is the 0.03472 meters, or the side length of the triangle that is formed by the two charges

This force is = 9.321 * 10 ^ -5 N

x-component of tension, which is T * sin10 or 0.00518 N

both forces are to the left, and the other force to the right is the electric field acting on the positive particle.

So -0.02985 N – 0.00518 N + F = 0

F q2 on q1 tension due to electric field

Set equal, you get the force due to electric field is equal to 0.006115 N

or 6.115 * 10 ^ -6 kN

since F = E / Q, we can multiply this F by Q2 and get the answer, right?

(6.115 * 10 ^ -6 kN) * (6.00 * 10 ^ -8 C) = 3.669 * 10 ^ -13 kN/C

Wrong answer…what’s the flaw in my logic? Thanks in advance