What is the force between two balloons with a negative charge of 1.6 × 10−10 C if the balloons are 0.05 m apart?

From Coulomb's Law it is possible to predict what the electrostatic force of attraction or repulsion between two particles will be according to their electric charge and the distance between them.

From Coulomb's Law, the electric force with which two point charges at rest attract or repel each other is directly proportional to the product of the magnitude of both charges and inversely proportional to the square of the distance that separates them:

[tex]F=k\frac{Qq}{d^{2} }[/tex]

where:

F is the electrical force of attraction or repulsion. It is measured in Newtons (N).
Q and q are the values of the two point charges. They are measured in Coulombs (C).
d is the value of the distance that separates them. It is measured in meters (m).
K is a constant of proportionality called the Coulomb's law constant. It depends on the medium in which the charges are located. Specifically for vacuum k is approximately 9×10⁹ [tex]\frac{Nm^{2} }{C^{2} }[/tex].

The force is attractive if the charges are of opposite sign and repulsive if they are of the same sign.

Force between two balloons

In this case, you know that two balloons have a negative charge of 1.6×10⁻¹⁰ C and the balloons are 0.05 m apart.

Replacing in the Coulomb's Law, you get:

[tex]F=9x10^{9} \frac{Nm^{2} }{C^{2} } \frac{(-1.6x10^{-10} C)x(-1.6x10^{-10} C)}{(0.05 m)^{2} }[/tex]

Solving:

[tex]F=9x10^{9} \frac{Nm^{2} }{C^{2} } \frac{2.56x10^{-20} C^{2} }{(0.05 m)^{2} }[/tex]

[tex]F=9x10^{9} \frac{Nm^{2} }{C^{2} } 1.024x10^{-17}\frac{ C^{2} }{m^{2} }[/tex]

F= 9.216×10⁻⁸ N

Finally, the force between the two ballons is 9.216×10⁻⁸ N.

Learn more about Coulomb's Law:

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