Question

If the charged rod is brought close to but not allowed to touch the neutral conducting sphere

Answer 1

Charging by induction occurs when a charged rod is brought near a neutral sphere, causing the sphere to polarize and, if grounded, to gain a net charge opposite to that of the rod without direct contact.

Step-by-step explanation:

Charging by Induction Explained

When a positively charged rod is brought close to, but not touching, a neutral conducting sphere, the process of charging by induction can occur. Initially, the neutral sphere becomes polarized, meaning the negative charges are attracted towards the rod, and the positive charges are repelled to the far side. If the sphere is then grounded, a conducting path to the Earth allows electrons to move to or from the sphere. This compensates for the shift in charge created by the nearness of the charged rod. When the connection to the ground is removed while the charged rod is still nearby, the sphere ends up with an excess of charge opposite to that on the rod. Once the rod is removed, the sphere retains this net charge. This is a classic physics demonstration showing that charging an object doesn't always require direct contact with a source of charge.

Answer 2

The charges in the neutral conducting sphere will redistribute themselves, with the side of the sphere closest to the charged rod experiencing an induced opposite charge and the opposite side developing an induced like charge.

Step-by-step explanation:

When a charged rod is brought close to a neutral conducting sphere, the charges in the sphere respond to the presence of the external charge. According to the principles of electrostatic induction, the electrons in the sphere are attracted to the charged rod, causing them to move towards the side of the sphere facing the rod. This migration of electrons results in an induced positive charge on the side of the sphere facing the rod.

Simultaneously, the electrons on the far side of the sphere move away from the charged rod, creating an induced negative charge on the opposite side of the sphere. The redistribution of charges aims to minimize the electric potential difference between the sphere and the charged rod. While the sphere as a whole remains neutral, this induced charge separation allows the neutral sphere to experience a net attraction toward the charged rod.

In mathematical terms, the induced charge, Qᵢₙᵤₛ, can be expressed using the formula Qᵢₙᵤₛ = -Qₒ(1 -
`e^-^d^/^λ`), where Qₒ is the charge of the rod, d is the distance between the rod and the sphere, and λ is the decay constant. This equation illustrates how the induced charge varies with the distance and the charge of the rod, providing a quantitative understanding of the electrostatic induction process.

Complete Question:

If a charged rod is brought close to but not allowed to touch a neutral conducting sphere, what happens to the charges in the sphere?