Question

You bring a negatively charged rubber rod close to a grounded conductor without touching it. Then you disconnect the ground. What is the sign of the charge on the conductor after you remove the charged rod? a) negative d) cannot be determined from the b) positive information given c) no charge

Short answer

a) Positive b) Negative c) No charge d) Both positive and negative Answer: c) No charge

Step-by-step solution

Analyzing the initial situation

Initially, we have a negatively charged rubber rod and a grounded conductor. When we bring the rod close to the conductor, the electrons in the conductor will be repelled by the negatively charged rod, causing the conductor's electrons to move away from the rod. This will result in one side of the conductor becoming positively charged, while the other side remains negatively charged.

Disconnecting the ground

Now we disconnect the ground from the conductor. By doing this, we essentially "trap" the charges on the conductor since there is no longer any external path for the charges to flow to/from the conductor. Thus, the charges on the conductor remain as they are when the ground is disconnected.

Removing the charged rod

When we remove the negatively charged rod from the vicinity of the conductor, the electrons in the conductor will try to redistribute themselves uniformly across the surface of the conductor. However, since the conductor was grounded, the positive and negative charges on the conductor are balanced, which means that the conductor remains neutral overall even after removing the charged rod. So, the correct answer is: c) no charge

Key concepts

Charging by Induction

Charging by induction is a method used to charge an object without direct contact. In this process, a charged object is brought near but not touching a neutral conductor. The presence of the charged object causes the charges in the conductor to rearrange: opposite charges are attracted towards the closer side, while like charges are repelled to the far side. This separation creates a polarization of charge within the conductor.

For instance, if a negatively charged rod is brought close to a neutral conductor, the free electrons in the conductor are repelled, and the area nearest the rod becomes positively charged. The key to induction is that the object causing the charge separation does not physically touch the conductor, which would lead to a transfer of charge.

Grounding in Electrostatics

Grounding in electrostatics is an essential concept that involves connecting an object to the Earth with a conducting wire or similar connection. The Earth is considered to be an infinite reservoir of charge. When an object is grounded, charges can move freely between the Earth and the object. Grounding can neutralize a charged object or facilitate the redistribution of charges.

During the process of charging by induction, grounding plays a critical role. By providing a pathway for charge to enter or leave the conductor, grounding helps in establishing the new charge distribution. For example, if a positively charged object is grounded, electrons from the Earth will flow onto the object, neutralizing some or all of the positive charge.

Charge Distribution

Charge distribution refers to how electric charges are arranged on a conductor. When a conductor is charged or placed in an electric field, charges within it move until they reach an equilibrium state. This state is such that the charges on the surface of the conductor will spread out to achieve a configuration where the repulsive forces between identical charges are minimized. Typically, in a static situation, charges reside only on the surface of a conductor.

In a case where a negatively charged rod is brought near a conductor, the charge distribution changes, and a separation of charge occurs within the conductor. When grounding is removed, the charge distribution present at that moment is locked in place due to the absence of a path for charge movement.

Conductors in Electrostatics

Conductors are materials that allow the free movement of electric charge. In electrostatics, conductors have properties that lead to unique behaviors under the influence of electric charge and electric fields. When a conductor is exposed to an external electric field, the free electrons move so as to cancel the field inside the conductor, resulting in zero electric field within the bulk material.

The exterior charge distribution on a conductor in electrostatic equilibrium is also affected by its shape. Charges tend to accumulate at points or edges where the curvature is greater, as the electrical potential energy is lower in these areas. Hence, sharp points on conductors will have higher charge densities and, consequently, greater electric fields.