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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).

Wikipedia article

Wikipedia article

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  • $\begingroup$ For the ungrounded object, the induced charges are equal to each other, but to the external charge causing the effect. $\endgroup$
    – Spirko
    Commented Dec 15, 2015 at 15:02

3 Answers 3

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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.

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The charge is induced inside an conductor so as to balance the electric field of the external charge.In steady state condition electric field inside the conductor is always zero,external electric fiels is cancelled by the induced charges on the surface of the conductors.

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If a conductor is ungrounded, then the charge on the conductor cannot change (unless touched by an electrically charged object).

Now, we know that every charge has electric field around it. So, if a charge is brought near an ungrounded conductor, (we are assuming that the conductor is uncharged), the will tend to develop electric field inside the conductor. But, we know that we cannot have any electric field inside any conductor, so the charges in conductor will align themselves so as to neutralize the electric field inside it. (But, the net charge inside the conductor is still zero).

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