Electric fields

What is the unit Farad a measure of?

Capacitance

What can we assume the relative permittivity of air is?

What can we assume the permittivity of air is?

1

the same as a vacuum (8.85 × 10^-12)

Where do we consider all charge of a spherical object to act?

At the centre

What is the key comparison to make between gravitational and electrostatic force at the subatomic level?

Electrostatic forces are approximately 10³⁹ times greater than gravitational therefore gravitational forces are negligible

What is relative permittivity? (the equation)

ε_r = ε / ε₀

Where ε_r is the relative permittivity,

ε is the material permittivity,

ε₀ is the permittivity of free space

Define Electric field strength

The force per unit positive test charge at a point in the field

Why does moving a positive charge against the electric field increase its potential?

Work must be done ON the charge against the opposing force due to the field.

Doing work on an object increases its total energy.

Hence its electric potential energy increases.

Hence its electric potential increases

Which equation have you got to be able to derive for electric fields?

Derive this equation

W = QV

E = F/Q and E = V/d

F/Q = V/d

Fd = QV

W = QV

Why does a charged particle follow a parabolic trajectory in an electric field if it enters the field at a right-angle to the field?

The initial velocity is at a right angle to the field (e.g. horizontal).

There is no horizontal force hence this velocity is constant.

The field exerts a force on the charged particle in the vertical direction.

This force is constant and (since mass is also constant) this means the acceleration is constant.

Acceleration in one direction and a constant velocity in the other results in projectile motion, hence a parabolic curve is followed.

Define “Absolute electric potential”

The work done per unit positive charge moving it from infinity to a given point in the field.

True or False? The electric potential around a charge is ALWAYS negative? Why/ Why not ?

FALSE

The electric potential is a measure of the work done moving / per positive test charge, by an external force, from infinity to a point in the field.

Moving a positive charge towards a negative charge will not require work to be done on the test charge, instead the test charge does work, hence negative potential energy and negative potential.

Moving a positive charge towards a positive charge will require work to be done on the test charge hence positive potential energy and positive potential

Define electric potential difference

The work done per unit charge moving it from one point to another in an electric field

If we connect an uncharged capacitor to a cell for charging, why is only 50% of the total energy supplied by the cell actually gained by the capacitor?

Energy transferred by cell = QV

Energy gained by Capacitor = ½ QV

Hence the other half is dissipated as thermal energy

How is charge stored on a capacitor?

Connect capacitor to EMF source

Electrons are repelled from negative terminal of source, thus build on one of the capacitor plates.

The positive terminal of source attracts electrons from the other plate.

Likewise, the negative plate repels electrons from the second plate.

Second plate now positive.

Hence charge stored on capacitor.

What happens to Current, Charge, and Potential difference through/ across the capacitor when charging?

The p.d across capacitor is initially 0 then increases overtime, hence p.d. across resistor is initially greatest and decreases overtime. Since V=IR this means that I decreases overtime.

Charge increases overtime.

What is the equation for V at time t across a capacitor?

Why is it not in the data booklet?

V = V₀ (1 - e^{(-t / RC)} )

Capacitance is constant hence V is directly proportional to Q so changes in the same way

What happens to Current, Charge, and Potential difference through/ across the capacitor when discharging?

Charge stored decreases exponentially

Hence p.d. across capacitor decreases exponentially

Hence p.d. across resistor decreases exponentially

Hence current (since V=IR) decreases exponentially

What is the equation for the change in current and the change in p.d. through/across a capacitor during discharging?

Why are they not on the data sheet?

V = V₀ e^{(-t / RC)}

I = I₀ e^{(-t / RC)}

They both follow the same decay curve as charge which is given on formula sheet

What does Q₀ indicate in the charging and the discharging formulae?

In charging : the maximum storable charge

in discharging : the initial / maximum storable charge

When T = RC, what percentage of the initial charge are you left with during the discharge of a capacitor? Why?

37%

e^-1 = 0.37

In terms of RC, what is the time needed for charge to drop to half its initial value during discharge?

Q₀ / 2 = Q₀ e^{(-t / RC)}

cancel Q₀

log and rearrange

T_1/2 = 0.69 RC

What does “Area of overlap” refer to when discussing optimal capacitors?

The Surface areas could be e.g. 100 units but if both plates are shifted slightly sideways then only e.g. 60 units may be facing each other hence the area of overlap is 60 not 100

Why do we use a dielectric?

What are polar molecules and how do they behave in capacitors?

To minimise the electric field strength thus minimis p.d. thus increase C.

molecules with a positive and negative end. They align in an electric field and produce an opposing electric field, reducing the resultant field strength

What is another name for relative permittivity?

Dielectric constant