Electric baubles

The interaction between the balls can be described by the Coulomb's law:

where q₁ and q₂ stand for the electric charge, r r is the distance between them, and the electrostatic constant equals k = 1/4pe₀= 9·10⁹Nm²/C².

In principle, Coulomb's law describes the interaction of point-like charges, but the charge distributed in a uniform way on the ball's surface is equivalent to a point-like charge placed in the centre of the sphere.

Let's calculate the force of the interaction between the spheres. We can evaluate the charge of the balls from their electrical capacity. The capacity of a sphere is determined by the equation C=R/k, where R is the diameter of the sphere. The meaning of the electrical capacity is as following: the capacity is 1 farad (F), if the electrical charge of 1 coulomb (C) generates the electrical potential of 1 volt (V).

The piezoelectric lighter generates voltages up to 10 keV, but the capacity of Christmas balls is very small (for balls with 4 cm diameter their capacity is about 0,4·10^-11 F). As a result, the charge on each ball is small (4·10^-8C). The interaction force between two charged balls positioned at a distance of 5 cm (measured between their centres) is also very small (1,4 mN), while the deviation from the vertical position by 1,5^o (i.e. by 0.5 cm for a ball attached on the 20 cm long wire) for the ball of 5 g mass requires 1,2 mN. Therefore, in order to observe collisions, the balls must be positioned really close.

If a third ball is attached to one of the poles of the piezoelectric lighter we observed that two electric charges of the same sign repel each other and two of different signs - attract each other.