Electrostatic Induction and Charge Conservation

Steps:

• Uncharged spheres X and Y touch, forming a single conductor with total charge zero.
• Positive rod near X attracts electrons to X's near side, leaving positive charge on Y.
• Electrons flow from Y to X, giving X net negative charge and Y net positive charge of equal magnitude.
• Spheres separate while rod is near, trapping opposite charges; total charge remains zero.

Why C is correct:

• Charge conservation law requires total charge zero, so Q_Y = -Q_X, meaning equal magnitude opposite signs.

Why the others are wrong:

• A: Y gains positive charge from electron loss, not negative.
• B: Magnitudes equal due to conservation, not smaller on Y.
• D: Magnitudes equal due to conservation, not larger on Y.

Final answer: C