Electric potential and equipotential surfaces

Positive test charge in the electric field experiences electric force. Moving against the E-field means that work need be done against the force. The work equals to the increase of electric potential energy of the test charge.









As potential energy describes work done to place the charge in the field, the electric potential describes the field itself. For a radial field of spherical charge (no E-field inside the sphere):

• Equipotential surfaces analogous to height contours in the gravity field. Perpendicular to electric field at any point
• No work need to be done in moving a charge along the surface (no displacement in the direction of E-field)
• Potential decreases in the direction of electric field
• Potential is zero infinitely far away from the source of radial field and at any earthed point.

Consider homogenous E-field between two parallel plates separated by distance d. What is the work done in moving charge Q over the potential difference V? If the bottom of the thundercloud and the Earth surface made up the plate pair separated by 1500 m, what would be the potential difference if the electric field was measured to be 25 kN/C.

Electric Field and Coulomb

Stationary electric charge creates static electric field (like mass creates gravitational field).

The geometry of the field depends on the geometry and charge distribution (point, (-s), sphere, line, plate, dipole...)

E-field is described by field lines (here point charges):

• At any point the direction of E-field is a) tangential to field line b) equal to the direction of electric force experienced by a tiny positive test charge.


• Strenth of the field corresponds to the density of field lines.

Coulomb law gives the strength of electric force between two point or spherical charges. Try here if the force obeys Coulomb law.

Electric charge

Any charge (for us..) is a multiple of an elementary charge (-e for electron, +e for proton).

Two ways to create electric charge:

1. Charging by friction. In contact, some atoms (materials) give away an electron more easily than others. Try brushing a sweater by a balloon.
2. Charging by induction. What happens if you move the balloon close to the wall?
   
   

Earthing means connection to infinite source/sink of free electrons.
There is eather attraction or repulsion between two electric cahrges. Can you state the signs of the unknown charges?

Malus and Brewster

In EM-wave, E-field oscillates perpendicular to the propagation.

• Unpolarized wave: E-field oscillates in all possible directions on the plane


• Polarized wave: E-field oscillates along a line (aka linearly or plane polarized)

Polarizer transmits the the component of E-field parallel to its transmission axis. And cuts 50 % of the intensity of unpolarized light.

Malus law: Set the transmission axes of the first and the third polarizers perpendicular to each other. How would you orientate the middle polarizer to have maximum intensity received in the detector? Can you proof it theoretically?

Brewster law: Reflected light is completely polarized if there a right angle between reflected and refracted components. Otherwise it is partially polarized. Rotate the View Angle and take a look to the two components.

Resolution and Rayleigh

Resolution is the minimum separation of two distinguishable objects in an image. Due to wave nature of light, the images get meshed i.e. the diffraction patterns overlap.

Rayleigh criterion: The two images are resolvable if the center peak of one image is exactly over the first minimum of an another image.

Take a look to see how different variables affect to the resolution of optical device.

On a dark night you look down a deserted road and see a distant light growing brighter, brighter... Then it splits into two distinct points of light: the headlights of a car coming towards you! At that moment, how far away is the car?

PRE-IB home practical on thermophysics

Cooling rate

The aim of the practical is to investigate the cooling rate of the tea sample. The temperature (T) of the sample is measured as a function of time (t).

1. The measurement is done at room temperature. Use boiling water to have high initial temperature.
· Take two identical mugs and fill them with 1 dl and 2 dl of tea.
· Read the temperature of the samples every 5 min for over an hour time interval.
· Remember to read the room temperature.

2. Repeat the two measurements outside. Remember to have the same mug and the same initial temperature. Measure the outside temperature.

3. Plot all the data in one (t,T) -system of coordinates.
· Indicate the different data sets
· Draw lines of best fit by eye to the data sets
· Determine the average cooling rate (unit: °Cs-1) for each sample
· Determine the cooling rate at the time t = 0,5 h for both 2 dl samples.

4. Answer briefly:
· How does the cooling rate change as a function of time?
· How does the mass affect on the cooling rate?
· How does the outside temperature affect on the cooling rate?
· Can you explain the shape of the curve?
· Are there any other variables affecting to the cooling rate? How would you investigate their contribution?

Single slit diffraction

Diffraction takes place at any slit, obstacle, edge... Relative size of aperture to the wavelength defines the amount of diffraction in a slit.

The diffraction pattern consist of bright and dark fringes:

• Bright due to constructive interference: path difference between the waves is a multiple of wavelength (central fringe, exactly zero)


• Dark due to destructive interference: path difference between the waves is a multiple of half wavelength (first dark fringes around central fringe, exactly one half of a wavelength).

Check the relationship between the location of dark fringes, wavelength and aperture.