Alternating current (AC)

AC means that the electric current (voltage) is changed both in direction and in magnitude as a function of time. Sinusoidal type is the most common.

In generator (dynamo) the relative orientation of the magnet and the loop is changed leading to change in magnetic flux. Note the two affects of change in rotational speed to the induced current.

Sinusoidal signal is produced by a loop rotating at constant angular is speed in a uniform magnetic field. The magneitude varies between peak values, r.m.s. value being the effective value.

In the AC circuit the power dissipated (to heat etc) in the resistor varies as a function of time, since the current varies. If the mean power over one cycle was equal to the resistor placed in the DC circuit, the DC current would be equal to the r.m.s. value of the AC current.

Hence, if a resistor of 50 ohm is placed in DC circuit it produces heat at the rate of 50 W when 1 A current flowing. In an AC circuit the same 50 W is produced by the same resistor if approximately 1,4 A in peak value is flowing.

Home practical on water flow

PRACTICAL ON THE MOTION OF WATER SURFACE

The aim of the practical is to study the speed of the water surface
in the bottle.


1. Take a plastic bottle which is as cylindrical as possible. Fill the cylindrical part with water and place it standing next to the water sink.

2. Drill a tiny hole (diameter some mm’s) to the wall of the bottle.

3. Let the water flow from the hole and measure the height of the surface as a function of time. Do it as carefully as possible with repetitions. Use cylindrical part of the bottle.

4. Draw height as a function of time.

5. Use the graph to determine the average speed of the water surface over the time period it takes the bottle to empty.

6. Determine the instantaneous speed of the water surface at the time
instant half of the bottle is empty.

7. Make a report on the practical. Remember to
· introduce the instruments
· table the data (units)
· label the axes, title the graph etc.
· show your calculations
· remember hypothesis, conclusion and evaluation of the practical.

Deadline: By the last lesson before exam week.

Lenz law

Lenz law determines the direction of induced electric current in the loop (minus sign in the Faraday law).

An induced current is always in such a direction as to oppose the motion or change causing it.

• If the flux increases, the induced magnetic flux is to decrease the total flux.
  
• If the flux decreases, the induced magnetic flux is to increase the total flux.

The Lenz law is easily understood by means of moving metal rod lying on the U-shaped conductor. Use right hand rule to deduce the direction of e.m.f. The inudced flux is here to out from the page, to oppose the increase of magnetic flux in to the page.

Deduce the direction of induced current in the following cases:

1. Bar magnet, 2. Metal ring, 3. Metal rod

Lenz law is an extension of Newton 3. law applied to electromagnetism. The induced B-field tries to oppose the ultimate reason to the change of the flux. For example:

1. Non-magnetic copper ring induces the magnetic force that bounces back the falling bar magnet and act as counter force to gravity.
2. Magnetic force due to induced eddy currents brakes the fall of a magnet inside the copper tube. Play a video.

Faraday's law

Temporally changing magnetic flux through a conductive loop creates (induces) electromotive force (and current) in the loop. Electromotive force is proportional to negative rate of change of the flux. This is Faraday's law of induction.

In 1831 Michael Faraday was able to show that changing electric current in primary coil creates changing magnetic field that induces current in secondary coil pierced by the same magnetic flux. As a result induced magnetic field was detected by a compass placed in the secondary coil.

The flux changes if B or A or angle or N or all change as a function of time, try with Pick up coil. The brightness of the lamp indicates the strength of the induced current. What about if you vary the rate of change?

Estimate the electric current (GI-current) induced in 400 kV transmission line in the case the vertical component of the geomagnetic field is decreassing from 48400 nT to 47180 nT in a minute. The transmission line makes a polygon in the Southern Finland as shown below. The resistance of the line is 0,9 mohm/km.

Moving charged particle experiences magnetic force

Right-hand rule is one way to remember the direction of magnetic force on charged particle. Current is in the direction of moving positive charge.

Hence, magnetic field exerts magnetic force on the rod carrying electric current.

Definition of 1 A electric current is based on the magnetic force!

The force is perpendicular to both B-field and velocity (cross-product in the formula) and does not increase the speed but change the direction of velocity at any moment. The particle begins to undergo circular path. Try how the different variables affect to the Larmor radius.

Can you conclude anything about the charges and masses of the four particles in the graph below?

Magnetic field

Permanent magnets (bar) or electric magnets (straight wire, solenoid,...) create magnetic field. Moving electric charge (current) gives rise to magnetic field. Unlike electric field lines, the magnetic field lines are closed loops i.e. no magnetic monopole exists. There are always both South pole and North pole.

The magnetic field at any point:

• direction tangential to field line and towards South pole (outside the magnet)


• strength proportional to density of field lines (also called magnetic flux)
  

The geomagnetic field due to plasma streams (volcanic electric currents) inside the Earth and the field geometry pretty similar to the field of gigantic bar magnet. The separation between geomagnetic south and geographic north is about 11 degrees. Solar plasma flow (solar wind) reshapes the dipole field:

In the presence of many fields, the total field is a vector sum of the component fields.

Electric current

The electric current is carried by moving electric charges (free electrons in metals) driven by external electric field (potential difference). The strength of the current depends on

• Number of free electrons in bulk motion
  
• Speed of the bulk motion (typically some cms in an hour)
  
• Collisions between the atoms in thermal motion

Due to the collisions, electrons loose kinetic energy i.e. electrical energy is transformed thermal energy (power dissipation). To maintain the current, work needs to be done at the same rate inside the power supply (cell, battery etc).

The lamp illuminates in five of the following cases. Which?