Question

Two lightweight metal spheres are suspended near each other from insulating threads. One sphere has a net charge; the other sphere has no net charge. The spheres will a) attract each other. b) exert no net electrostatic force on each other. c) repel each other. d) do any of these things depending on the sign of the charge on the one sphere.

Short answer

Answer: The two spheres will attract each other.

Step-by-step solution

Understand the properties of charged and uncharged spheres

In this situation, we have two spheres. One sphere has a net charge, which means it has either an excess or deficiency of electrons, resulting in a positive or negative electric charge. The other sphere has no net charge, meaning it has an equal number of electrons and protons.

Consider the behavior of charged objects

When two charged objects are near each other, they exert electrostatic forces on each other. These forces can be attractive or repulsive, depending on the type of charge each object has. Similar charges (positive-positive or negative-negative) will repel each other, while opposite charges (positive-negative) will attract each other.

Analyze the interaction between the charged sphere and the uncharged sphere

The uncharged sphere has an equal number of electrons and protons. When the charged sphere comes near the uncharged sphere, the charged sphere's electric field will interact with the charges in the uncharged sphere, inducing a polarization effect. This means that the charged sphere will push or pull the charges in the uncharged sphere, creating a temporary net charge distribution in the uncharged sphere.

Determine the type of electrostatic force between the spheres

Now that the uncharged sphere has a temporary net charge distribution because of the charged sphere's influence, the two spheres will exert electrostatic forces on each other. Since the temporary net charge distribution in the uncharged sphere is opposite to the net charge of the charged sphere, the two spheres will attract each other. So the correct answer is: a) attract each other.

Key concepts

Charged and Uncharged Spheres

When we observe the interaction between two spheres, understanding the difference between charged and uncharged spheres is crucial. A charged sphere holds an excess or deficiency of electrons, which gives it a net electric charge that can be either positive or negative. Conversely, an uncharged sphere has an equal number of protons and electrons, thereby having no net electric charge.

The significance of a sphere being charged or uncharged lies in its ability to exert and respond to electrostatic forces. Charged spheres can generate an electrostatic field around them, affecting other nearby charged or uncharged objects. However, an uncharged sphere normally does not interact with other uncharged objects because it does not have an electrostatic field of its own. Yet, it can still be influenced by the presence of a charged object, leading us into the fascinating phenomenon known as the polarization effect.

Behavior of Charged Objects

The behavior of charged objects in proximity to one another is governed by the fundamental laws of electrostatics. Charged objects can experience two types of electrostatic forces: attractive and repulsive. The rule of thumb here is straightforward: like charges repel, whereas unlike charges attract. For instance, two negatively charged objects will push away from each other, just as two positively charged objects would. On the other hand, a positive charge near a negative charge would pull them together.

These interactions are not just academic concepts; they have practical applications in various fields, such as inkjet printing and electrostatic precipitators used for air purification. Understanding the behavior of charged objects is thus not only essential for physics students but also for engineers and scientists working in technological advancements.

Polarization Effect

The polarization effect is quite fascinating; it's what occurs when an uncharged object comes under the influence of a charged object's electric field. This effect rearranges the charges within the uncharged object, such that they shift to align with the external electric field. Electrons move towards the positive charge, while regions of positive charge are generated as electrons move away from the side facing a negative charge.

When an uncharged metal sphere is exposed to this electrostatic field, the free electrons within the metal will either move toward the sphere's side facing the positive charge, or away from it if the charge is negative. This induced charge separation creates a temporary dipole within the sphere, resulting in a net electric field that can now interact with the charged sphere, leading to attraction, despite the sphere originally being uncharged. This concept is not only pivotal in understanding the exercise problem but also in the design of materials and devices that use electrostatic properties for functionality, such as sensors and actuators.