Ananya looked up at the rain-streaked window. Somewhere in the gap between the perfect conductor of theory and the real metal of the lab, a tiny, ghostly repulsion lived—an inverse transient that no experiment had ever been fast enough to see.
But tonight, she did the derivation by hand, step by step, the way Satya Prakash did it: no approximations, no vector shortcuts, just the brutal geometry of Coulomb’s law integrated over induced surface charges. satya prakash electricity and magnetism pdf
The problem was problem 3.17 in the old Satya Prakash textbook—the dog-eared, coffee-stained, 1987 edition her own professor had gifted her. It read: Ananya looked up at the rain-streaked window
“A point charge q is placed at a distance d from the center of an uncharged conducting sphere of radius R (R < d). Find the force on the charge. Verify that the force is always attractive, no matter the sign of q.” The problem was problem 3
She’d solved it a thousand times. Method of images: place an image charge q’ = -qR/d at distance b = R²/d from the center. Force = attractive, proportional to 1/(d² - R²)². Done.