If we rub a balloon on our hair, the balloon sticks to a...

If we rub a balloon on our hair, the balloon sticks to a wall or ceiling. This is because the rubbing transfers electrons from our hair to the balloon, giving it a net negative charge. When the balloon is placed near the ceiling, the extra electrons in it repel nearby electrons in the ceiling, creating a separation of charge on the ceiling, with positive charge closer to the balloon. Model the interaction as two point-like charges of equal magnitude and opposite signs, separated by a distance of $500 \mu \mathrm{m}$. Neglect the more distant negative charges on the ceiling. (a) A typical balloon has a mass of $4 \mathrm{~g}$. Estimate the minimum magnitude of charge the balloon requires to stay attached to the ceiling. (b) since a balloon sticks handily to the ceiling after being rubbed, assume that it has attained 10 times the estimated minimum charge. Estimate the number of electrons that were transferred to the balloon by the process of rubbing.

Key Concepts

Charge Quantization

Charge quantization refers to the fact that electric charge exists in discrete units, typically in multiples of the elementary charge found on electrons. This concept is important when analyzing how many electrons are transferred to an object during static electricity phenomena, enabling calculations that link measured charge values to a count of electrons.

Gravitational Force

Gravitational force is the attractive force that the Earth exerts on objects due to their mass, calculated as the product of mass and gravitational acceleration. When assessing the conditions required for a charged object to remain suspended, comparing the electrostatic force to the gravitational force is critical to ensure the upward force can counterbalance the downward pull of gravity.

Frictional Charging (Triboelectric Effect)

The triboelectric effect describes the process by which certain materials become electrically charged after they come into frictional contact with a different material. In the context of everyday phenomena like a balloon sticking to a wall, friction causes electrons to be transferred, leading to a net charge imbalance that results in observable electrostatic interactions.

Coulomb's Law

Coulomb's Law quantifies the force between two point charges, stating that the magnitude of the electric force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. This law is essential for calculating the electrostatic forces in systems where charged objects interact, such as estimating the force needed to overcome gravitational pull.

Electrostatic Force

Electrostatic force is the force of attraction or repulsion between objects due to their electric charges. In problems involving charged objects such as a balloon and a ceiling, this force determines whether the object can overcome other forces like gravity and remain suspended. It is foundational to understanding interactions in static electricity.

Transcript

00:01 Hello, everyone.

00:01 In this problem, we're asked to investigate a balloon sticking to the ceiling.

00:06 So we're told that as we rub the balloon against our hair, we essentially charge it, giving it our transferring electrons from our hair to the balloon.

00:15 And then as we push this balloon close to the ceiling, it pushes out the electrons from the ceiling or away from the surface of the ceiling, generating a net positive charge in the ceiling, which then attracts the negative charges on the balloon.

00:29 So we're asked to model this behavior by basically assuming that the balloon and the charges in a balloon and the charges on the ceiling are point charges that are separated by some distance d.

00:42 So we're told that this distance we can assume to be 500 micrometers, so 500 times 1030 minus 6 meters.

00:47 And we're told that the balloon has a mass of 4 grams, i .e.

00:51 4 times 10 to minus 3 kilograms.

00:53 So what we have to find is the charge that the minimum charge that the balloon has to be charged with or it has to attain in order to be able to stick to the ceiling.

01:04 So what we're going to do is we're going to analyze the freeway diagram of the balloon, say that it is in equilibrium.

01:10 So if we look at the freeway diagram, the only force is acting on the balloon are the coolum force from the ceiling and the weight of the balloon acting down.

01:19 Now there, of course, there would be also a coulum force pushing down from the pushed away negative charges of the ceiling, but we're told that we can ignore that force.

01:30 So these are the only two forces acting...

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