Is it true that if a conducting object is not grounded, the nearby charge will induce equal and opposite charges in the conducting object?
It is mentioned on Wikipedia (electrostatic induction) but it is also mentioned that charges will appear such that the total electric field inside the conductor becomes zero.
My doubt is that which statement is true whether the charges induce such that the electric field inside the conductor becomes zero or the induced charge is equal in magnitude to the inducing charge (the charge which causes induction).
Best Answer
What happens is that for a conductor limited in real space and not grounded the net charge can't change (if is 0 it has to remain 0), so on the face towards the external charge it accumulates a charge to balance the electric field inside the conductor, but on the other face it accumulates a charge opposite in sign, to balance the net charge on the conductor.
If the conductor is unlimited in space (that happens only in physics exercise) the "other face" is moved to infinity, so also the charge that should balance that on conductor, and so if you integrate the charge density in space ($\mathbb{R}^3$ doesn't include the "infinity") you find a net charge on the conductor, but space-unlimited conductor don't really exist.