A metal sphere is placed on an insulating stand. A negatively charged rod is brought close to it. If the…

Analysis of the Question

This question tests your understanding of electrostatic induction and the process of charging by induction. You are asked to determine the final state of a metal sphere after it undergoes a specific sequence of interactions with a charged rod and an earth connection.

Concept Explanation: Charging by Induction

Charging by induction allows you to charge an object without touching it with a charged body. Here is the step-by-step physical process:

1. Induction: When a negatively charged rod is brought near the neutral metal sphere, the free electrons in the sphere are repelled to the far side of the sphere. This leaves the side near the rod with a net positive charge.
2. Earthing: When you connect the sphere to the earth (grounding), the repelled electrons (which are on the far side) flow into the earth because they are repelled by the rod and have a path to escape.
3. Breaking the Earth Connection: If you remove the earth connection while the rod is still held close, the sphere is now "trapped" with a deficiency of electrons.
4. Removing the Rod: Once the rod is taken away, the remaining positive charges redistribute themselves uniformly over the surface of the sphere.

Step-by-Step Solution

• Step 1: The negatively charged rod is brought near the sphere. The sphere polarizes: positive charges gather near the rod, and negative charges are pushed to the opposite side.
• Step 2: The sphere is earthed. The excess negative charges (electrons) on the far side flow into the earth.
• Step 3: The earth connection is removed. The sphere is now left with a net positive charge because electrons have left the sphere.
• Step 4: The rod is removed. The sphere remains positively charged.

Conclusion

Because electrons were removed from the sphere through the earthing process, the sphere is left with a deficit of electrons, which means it acquires a net positive charge.

Exam Tip: Always remember the "Opposite Rule" in induction: When charging by induction, the object being charged will always acquire a charge opposite to that of the inducing rod. Since the rod was negative, the sphere must become positive!