Topic 8.2 Conservation of Charge and the Process of Charging: apply conservation of charge to charging by friction, conduction and induction, and explain grounding and polarization.

What this topic is asking

The College Board (Topic 8.2) wants you to apply conservation of charge to the three ways objects become charged, friction, conduction and induction, and to explain grounding and polarization. The conceptual payoff is that no process ever creates or destroys net charge: charging only moves electrons around.

Conservation and quantisation of charge

Charge is also quantised: every charge is an integer multiple of the elementary charge $e = 1.60\times10^{-19}$ C, so $q = ne$. Charging an object means adding or removing whole electrons, which is why a neutral object that loses $N$ electrons acquires a charge of $+Ne$.

Charging by friction and conduction

Friction (or contact) transfers electrons when two different insulating materials are rubbed together. One material holds electrons more tightly, so it gains electrons (becomes negative) while the other loses them (becomes positive). The amounts are equal and opposite, conserving charge.

Conduction charges a conductor by direct contact with a charged object. Electrons flow until the two share the excess. For two identical conductors, symmetry forces an equal split: if charges $q_A$ and $q_B$ are brought into contact, each ends with $\dfrac{q_A + q_B}{2}$.

Charging by induction

Induction charges a conductor without ever touching it with the charged object:

1. Bring a charged object near (do not touch). Its field polarizes the conductor, drawing one sign to the near face and pushing the other to the far face.
2. Ground the conductor briefly. The charge repelled to the far side flows off to ground (or onto it from ground).
3. Remove the ground, then remove the charged object.

The conductor is left with a net charge of the sign opposite to the inducing object. No charge was transferred from the inducing object itself, so its charge is unchanged, again conserving the total.

Polarization: conductors versus insulators

A neutral object is attracted to a charged one because of polarization. In a conductor, free electrons migrate, building a net negative region near a positive charge and a net positive region far from it; the nearer, opposite charge is pulled more strongly than the farther, like charge is pushed, so there is a net attraction. In an insulator, electrons cannot travel far, but each molecule's charge distribution distorts slightly (the molecules become tiny dipoles), producing a weaker surface polarization and the same net attraction.

Try this

Q1. A neutral metal sphere is charged by induction using a positive rod. State the sign of the sphere's final charge. [1 point]

• Cue. Negative; induction leaves the sign opposite to the inducing charge.

Q2. Two identical conductors carry $+10$ nC and $-4$ nC. They are touched together and separated. Find the charge on each. [2 points]

• Cue. Total $= +6$ nC, shared equally, so each ends with $+3$ nC.