Electric Fields & Capacitance Review

Practice flashcards covering electric fields, Coulomb's law, electric potential, and capacitor charging/discharging based on the physics lecture notes.

What is an electric field?

An electric field is a region in which a charged body will experience a force.

What determines the direction of electric field lines?

Field lines show the direction of force that would be experienced by a small positive test charge if it were placed at that point in the field.

How is the relative strength of a field represented graphically?

The closer together the field lines are, the stronger the force.

Define equipotentials.

Equipotentials are lines perpendicular to field lines that join points with equal potential; no work is done on a test charge if it moves along an equipotential.

State Coulomb's Law of Attraction.

The force between two point-charges is directly proportional to the product of their charges and inversely proportional to the square of their separation.

What is the mathematical equation for Coulomb's Law in a vacuum?

F = \frac{1}{4\times\text{\pi}\times\text{\epsilon}_0} \times \frac{Q_1 \times Q_2}{r^2}

What is the value and unit of the permittivity of free space (\text{\epsilon}_0)?

\text{\epsilon}_0 = 8.85 \times 10^{-12} \, \text{Fm}^{-1}

Define electric field strength ($E$).

The force per unit charge that would be experienced by a small positive test charge.

What are the two common units for electric field strength?

$\text{NC}^{-1}$ or $\text{Vm}^{-1}$

What is the formula for electric field strength ($E$) in a radial field?

E = \frac{1}{4 \times \text{\pi} \times \text{\epsilon}_0} \times \frac{Q}{r^2}

What is the formula for electric field strength ($E$) in a uniform field between parallel plates?

$E = \frac{V}{d}$ where $V$ is potential difference and $d$ is the distance between plates.

What is the electric field strength inside a hollow charged sphere?

Zero.

Define absolute electric potential energy ($E_p$).

The work done in moving a charged object from infinity to that point in an electric field.

What is the formula for absolute electric potential energy ($E_p$)?

E_p = \frac{1}{4 \times \text{\pi} \times \text{\epsilon}_0} \times \frac{Q_1 \times Q_2}{r}

Define absolute electric potential ($V$).

The work done per unit charge in moving a small positive test charge from infinity to that point in the field.

How is the absolute electric potential ($V$) for a radial field calculated?

V = \frac{1}{4 \times \text{\pi} \times \text{\epsilon}_0} \times \frac{Q}{r}

Define capacitance ($C$).

Capacitance is the charge stored per unit potential difference across the plates of the capacitor ($C = \frac{Q}{V}$).

What does the gradient of a charge ($Q$) against potential difference ($V$) graph represent?

Capacitance ($C$).

How is the energy stored by a capacitor found from a graph of charge ($Q$) against potential difference ($V$)?

The area under the graph.

Provide three equations for the energy ($E$) stored by a capacitor.

$E = \frac{1}{2} \times Q \times V$, $E = \frac{1}{2} \times C \times V^2$, and $E = \frac{Q^2}{2 \times C}$

What is the formula for a parallel plate capacitor including relative permittivity (\text{\epsilon}_r)?

C = \frac{A \times \text{\epsilon}_0 \times \text{\epsilon}_r}{d}

What happens to the capacitance of a parallel plate capacitor when a dielectric is inserted?

The capacitance increases.

Define the time constant ($RC$) for a capacitor circuit.

The time constant is the time (in seconds) it takes for the charge (or potential difference/current) to fall to $1/e$ (approximately $37\%$) of its original value.

What is the 'half-life' formula for capacitor discharge ($T_{1/2}$)?

T_{1/2} = \text{\ln}(2) \times RC \times [0.69 \times RC]

How is the charge ($Q$) on a charging capacitor calculated at time ($t$)?

$$Q = Q_0 \times (1 - e^{-\frac{t}{RC}})$$

How many time constants ($RC$) are theoretically required to consider a capacitor practically fully charged or discharged?

$5 \times RC$, as only approximately $0.69\%$ of the charge/potential difference remains (or is left to gain).

According to Bailey (1960), what was the estimated charge of the Sun?

$$+1.5 \times 10^9 \, \text{C}$$

What fundamental force is involved when an alpha particle is scattered by a gold nucleus?

Electromagnetic.

How does absolute electric potential ($V$) relate to electric field strength ($E$) on a graph?

$V$ is related to $E$ by E = \frac{\text{\Delta}V}{\text{\Delta}r}, and \text{\Delta}V is the area under a graph of $E$ against $r$.

What is the purpose of a dielectric material in a capacitor?

It consists of polar molecules that align in the electric field, which reduces the potential difference for a fixed charge, thereby increasing capacitance.