Electric Circuits

The magnitude remains constant as it depends solely on the geometry of the space.

The magnitude decreases since higher charge density leads to mutual repulsion weakening the field.

The magnitude increases since stronger charge density creates stronger electric fields.

The magnitude is inversely proportional to charge density due to the inverse square law.

$\omega_{0}$ decreases

It doubles as well

No change to $\omega_{0}$

$\omega_{0}$ increases

V varies linearly with $r$ inside

V = zero everywhere inside

V = $\frac{kQ}{R}$

V = $\frac{kQ}{r}$ where $r < R$

There can be no simple relation between capacitance and energy without additional information about voltage or charge changes.

The energy stored in the capacitor halves since energy stored is proportional to the square of the charge over capacitance.

Energy remains unchanged since maintaining the same charge implies constant voltage, hence constant stored energy.

It doubles the energy stored since increased capacitance resources greater potential difference to maintain the same charge.

To provide a path for electricity to flow without resistance.

To limit the flow of current.

To convert electrical energy into light.

To store electrical energy.

Normal surface interaction relevant when moving freely in space

Centripetal Force provided by the Lorentz Force

Gravitational force, negligible compared to electromagnetic scenarios

Fictitious outward 'centrifugal' force that only exists in a frame of reference

Magnetic force does not act on particles unless there is motion in relation to the field

Transformer.

Resistor.

Capacitor.

Inductor.

The electrostatic force decreases since force is proportional to the inverse square of the distance between charges.

The electrostatic force remains unchanged as it is directly proportional to the product of the charges' magnitudes.

The electrostatic force increases because force is inversely proportional to the square of the distance between charges.

The electrostatic force decreases linearly with distance once a certain threshold distance is surpassed.

A cube that surrounds both conductors and has an edge parallel to the rod.

A plane perpendicular to the rod and cutting through the center of the shell.

A sphere centered at the midpoint between the two conductors.

A right hollow cylinder extending beyond the ends of both conductors that has the same radius as the point of interest.

The voltage across each component would remain constant regardless of frequency changes.

There would be no observable effect as LC circuits are independent of frequency changes.

The amplitude of voltage across each component would increase exponentially with frequency.

The voltage across each component would oscillate at increased frequencies without changing amplitude.