phys1702 w7 l4

Insulators: materials through which electrons cannot move freely.
Example from transcript: plastic pens rubbed with a sock become charged, but the extra electrons stay where they were placed because plastic is insulating.
If electrons could move freely in plastic, the excess electrons would spread across the surface and could even transfer to a finger, potentially leaving the pen neutral.
Conclusion: plastic is an insulating material.

Conductors allow electrons to move relatively freely (e.g., metals).
When excess electrons are placed on the surface of a spherical conductor, they do not stay bunched up; they distribute themselves uniformly across the surface due to repulsion and mobility.
This uniform distribution minimizes repulsion and creates an equipotential surface.

Setup: two identical conductive spheres, initially neutral, are brought into contact.
If a bunch of extra electrons is placed on the surface of the first sphere, they would spread to the second sphere after contact, until charges on the two spheres are equal.
Key principle: conservation of electric charge during the process.
When they touch, electrons flow from the sphere with higher electron density to the other until there is no incentive for further flow (i.e., the charges become equal).
Since the total net charge must be conserved and the spheres are identical, the total charge is split equally:
Q^{\prime}{1} = Q^{\prime}{2} = Q^{\prime}
Q{\text{total}} = Q{1} + Q{2} = 2Q^{\prime} \Rightarrow Q^{\prime} = \frac{Q{1} + Q_{2}}{2}
Special case: if both were initially neutral, Q{1} = 0, \; Q{2} = 0 \Rightarrow Q^{\prime} = 0, so each ends with zero net charge.

Scenario: one sphere has a negative charge Q1 (excess electrons), the other has a positive charge Q2 (deficiency of electrons).
Upon contact, electrons flow from the negatively charged sphere to the positively charged one until the charges on both spheres are equal:
Q^{\prime}{1} = Q^{\prime}{2} = Q^{\prime}
Conservation of charge gives:
Q{\text{total}} = Q{1} + Q{2} = 2Q^{\prime} \Rightarrow Q^{\prime} = \frac{Q{1} + Q_{2}}{2}
Interpretation: the final charge on each sphere is the average of the initial charges.

Example values from transcript: suppose the negatively charged sphere has charge Q{1} = -6\ \mu\text{C} and the positively charged sphere has Q{2} = +7\ \mu\text{C}.
Total initial charge: Q{\text{total}} = Q{1} + Q_{2} = -6 + 7 = 1\ \mu\text{C}
Final charge on each after touching:Q^{\prime} = \frac{Q{1} + Q{2}}{2} = \frac{1}{2} = 0.5\ \mu\text{C}
Result: both spheres end up with a positive charge of +0.5\ \mu\text{C} on each.
Visual takeaway: even though one sphere started negative and the other positive, once they touch and share charge equally, both end up with the same, here positive, net charge.

When two identical conducting spheres touch, charges redistribute to equalize the charges on both spheres.
The total charge is conserved:
Q{\text{total}} = Q{1} + Q{2} = Q^{\prime}{1} + Q^{\prime}_{2} = 2Q^{\prime}
Therefore, the final charge on each sphere is:
Q^{\prime} = \frac{Q{1} + Q{2}}{2}
If the total initial charge is positive, both final charges are positive; if negative, both final charges are negative; if zero, both remain neutral.
Important physical intuition: conductors allow charge mobility, insulators do not; contact enables charge transfer until electrostatic equilibrium (equal charges) is reached.

Link to conservation of charge: the net charge in an isolated system remains constant.
Equipotential concept: redistribution in conductors leads to equal potential across the connected bodies, which drives the flow of charge until equality is achieved.
Real-world relevance: charging by contact, capacitive coupling, and how charges distribute on conductors in devices like capacitors and charging cables.
Potential extensions: what happens if spheres are not identical? Final charges would not be equal; the shared charge depends on relative sizes and capacitances, and more advanced treatment involves solving for equal potentials with different geometries.