A positively charged rod X is brought near an uncharged metal sphere Y and is then touched by a finger with X…

Analysis of the Question

This question tests your understanding of electrostatic induction and charging by conduction (earthing). We are looking at what happens to the charge and potential of a neutral metal sphere when it is influenced by a charged rod and then grounded.

Concept Explanation

1. Induction: When a positively charged rod (X) is brought near an uncharged metal sphere (Y), the free electrons in the metal sphere are attracted toward the rod. This causes the side of the sphere closest to the rod to become negatively charged, while the side furthest away becomes positively charged.
2. Earthing (Touching with a finger): When you touch the sphere with your finger, you provide a path for electrons to flow between the Earth and the sphere. Because the positive charge on the far side of the sphere is "repelled" by the positive rod, electrons from the Earth flow into the sphere to neutralize that positive charge.
3. Result: Once the finger is removed, the sphere is left with an excess of electrons (a negative charge) that were drawn from the Earth.
4. Potential: The potential of an object is determined by its charge. Since the sphere now has a net negative charge, its electric potential is negative relative to the Earth (which is at zero potential).

Step-by-Step Solution

• Step 1: Rod X (positive) is brought near Sphere Y. Electrons in Y move toward X.
• Step 2: The far side of Y becomes positive.
• Step 3: Touching Y with a finger allows electrons from the Earth to flow into Y to neutralize the positive side.
• Step 4: Removing the finger traps these extra electrons on the sphere.
• Step 5: Sphere Y now has a net negative charge.
• Step 6: Because the sphere is negatively charged, its potential is negative.

Conclusion

The sphere gains a negative charge due to the flow of electrons from the Earth, and consequently, it acquires a negative potential.

Exam Tip: Remember the "Finger Rule" for induction: When you ground an object near a positive rod, it gains a negative charge. If you ground it near a negative rod, it gains a positive charge. The potential always follows the sign of the net charge on the object.