To give two metal spheres equal and opposite charges using a glass rod rubbed with silk, you can utilize the principle of induction. This method allows you to charge the spheres without direct contact, which is key to your scenario. Let’s break down the steps involved and address the question about the size of the spheres.
Charging Process Using Induction
Here’s how you can achieve the desired charging of the spheres:
- Initial Setup: Place the two metal spheres on their insulating supports, ensuring they are not touching each other.
- Bring the Charged Rod Near One Sphere: Take the glass rod that has been rubbed with silk, which will have a positive charge due to the transfer of electrons to the silk. Bring this rod close to one of the spheres (let's call it Sphere A) without touching it.
- Induction Effect: The positive charge of the rod will repel the positive charges in Sphere A, causing them to move away from the rod. This results in the near side of Sphere A becoming negatively charged and the far side becoming positively charged.
- Grounding Sphere A: While the rod is still close to Sphere A, connect Sphere A to the ground using a wire. This allows electrons to flow from the ground into Sphere A, neutralizing the positive charge on the far side and leaving Sphere A with a net negative charge.
- Remove the Ground Connection: Disconnect the wire from Sphere A while the rod is still nearby. This traps the negative charge on Sphere A.
- Remove the Rod: Finally, take the glass rod away. Sphere A now has a net negative charge.
- Charge Sphere B: Repeat the process with Sphere B, but this time bring the rod close to Sphere B without touching it. The same induction effect will occur, but since Sphere B is now isolated, it will acquire a net positive charge after grounding it while the rod is nearby.
Understanding the Role of Sphere Size
Now, regarding whether the spheres need to be of equal size for this method to work: the answer is no, they do not have to be the same size. The principle of induction relies on the distribution of charge rather than the amount of charge itself. However, the size of the spheres can influence how effectively they can hold and distribute charge.
- Charge Distribution: Larger spheres have a greater surface area, which can allow for a more uniform distribution of charge. This means they might hold a charge more effectively than smaller spheres.
- Induction Effectiveness: The distance between the charged rod and the spheres, as well as their size, can affect how strong the induced charges are. A larger sphere may experience a more pronounced effect due to its ability to redistribute charge more easily.
In summary, while the spheres do not need to be of equal size for the method to work, their size can influence the efficiency of the charging process. The key takeaway is that using induction allows you to charge the spheres without direct contact, and you can achieve equal and opposite charges regardless of their sizes.
