Electric Force, Field, and Potential

The creation of Faraday's cage for shielding sensitive experiments from external fields.

The formulation of Coulomb's law through torsion balance experiments by Charles-Augustin de Coulomb.

The development of the oil-drop experiment by Robert Millikan.

Benjamin Franklin's invention of the lightning rod and his taxonomy of positive and negative charges.

There is zero potential difference across each resistor due to internal resistance of wires connecting them being non-negligible compared to that of resistors themselves.

It varies inversely with respect to their distances from the voltage source.

It increases linearly from one end to another.

It remains equal for all resistors.

It increases because both factors proportionally raise voltage contributions from individual charges despite greater distances involved.

It decreases due to heightened mutual repulsion reducing net influence on surrounding electric field intensity at that point.

It remains constant as increased contribution from higher magnitude is precisely countered by diminished impact due to larger separation.

The change is indeterminate without specifying whether distance increase or charge magnitude has a greater proportional effect on potential.

$+2q$

$+8q$

$0$

$+4q$

Answering A implies minimal deviation since velocity component parallel remains constant while perpendicular component undergoes circular motion generating least outward radial movement.

Answering E overlooks sine function relating cross-product magnitude meaning maximal value attained half-way complete rotation not start/endpoints rendering option flawed regarding optimal theta choice yielding extreme radial migration.

Answering C could be considered right as it suggests calculating acceleration using centripetal motion equations given $θ = vB \\sin(θ)$ providing maximal radial force hence greatest displacement.

Answering D assumes entry path lies within plane containing B thus experiencing zero Lorentz Force leading smallest possible radius therefore incorrect asserting most significant radial shift.

Via induction as electromagnetic fields induce heat flow without direct contact.

Using advection as the warmer fluid circulates to replace cooler fluid around the rod.

Through conduction, as thermal energy transfers from the high temperature rod to the lower temperature water.

By radiation, emitting infrared waves from the rod to the water.

Joule (J)

Volt (V)

Coulomb (C)

Watt (W)

The smaller-radius conductor will have higher surface charge density.

Both conductors will have identical surface charge densities due to being spherical.

Surface charge density cannot be determined without knowing the exact charge in each conductor.

The larger-radius conductor will have higher surface charge density.

Use a uniform electric field model without considering edge effects and measure the change in electric field strength with varying plate charge.

Directly calculate permittivity by measuring potential difference across the plates for several fixed charges, ignoring fringing fields.

Measure capacitance versus plate separation for small separations and extrapolate to zero separation after accounting for edge effects analytically.

Connect different capacitors in series, measure total capacitance, and solve for individual capacitances assuming no fringe effects or plate size variations.

Capacitors store and release energy periodically without dissipation, contributing to phase shifting and filtering purposes.

Their sole purpose is to convert AC current into direct current, hence their inclusion is indispensable.

They actually dissipate some energy as heat similarly to resistors but much less efficiently, thus still useful.

Capacitors provide non-reactive loads compensating for power factor issues causing energy losses elsewhere inside the network.