Coulomb's Law (Electric Force) Video Lessons

Concept

# Problem: 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?

###### FREE Expert Solution

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

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

Coulomb's law:

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

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:

Tx = Tsin(10°)

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

Ty = 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.

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###### Problem Details

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?