The force exerted by an external electric field on the charged sphere is:

$\overline{){{\mathbf{F}}}_{{\mathbf{E}}}{\mathbf{=}}{\mathbf{\left|}}{\mathbf{q}}{\mathbf{\right|}}{\mathbf{E}}}$, where E is the electric field and q is the charge.

Coulomb's law:

$\overline{){\mathbf{F}}{\mathbf{=}}\frac{\mathbf{k}\mathbf{\left|}{\mathbf{q}}_{\mathbf{1}}\mathbf{\right|}\mathbf{\left|}{\mathbf{q}}_{\mathbf{2}}\mathbf{\right|}}{{\mathbf{r}}^{\mathbf{2}}}}$

From the figure given, the gravitational force, mg, acts in the downward direction.

Tension, T acts in the upward direction along the rope.

The x-component of T is in the negative x-direction and is given by:

T_{x} = Tsin(10°)

The y-component of T along the positive y-direction is:

T_{y} = Tcos(10°)

Since the spheres have opposite charges, the Coulombic force between them is attractive.

The force of attraction F on the second charge is along the x-direction.

The electric field is along the x-direction.

The identical small spheres shown in the figure on the right are charged to +100 nC and -100 nC. They hang as shown in a 100,000 N/C electric field. What is the mass of each sphere?

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