Properties of Waves

In this section, we will learn basic properties of waves. We have learned transverse and longitudinal waves in the last section. Now we use them and try to explain basic concepts of wave phenomena as; wavelength, velocity, amplitude, pulse, frequency.

Pulse:  one wave motion created at the spring.

Where; x is the pulse length and y is the amplitude (height of the pulse).

Wavelength: It is the distance between two points of two waves having same characteristics.

wavelength is shown with the greek letter "" and unit of it is "m". 

 Period: Time required for the production of one wave is called period. It is shown with letter "T" and its unit is "s". 

Frequency: It is the number of waves produced in a given unit of time. It is shown with letter "f" and its unit is "1/s".

Periodic Wave: If the wave source produces an equal number of waves in equal times, then this wave called a periodic wave.

 f=1/T

Velocity of the Wave: Velocity of the wave is constant in a given medium. However, if the medium is changed then the velocity of the wave is also changed.  We show velocity with "v" and its unit is m/s.

Waves

In this unit, we will discuss properties of waves and types of waves. Moreover, we will try to explain situations which can not be explained with light properties of matter. Disturbance of the shape of the elastic matters are transported from one end to other by the particles of that matter, we call this process  wave. Be careful, during the transportation, no matter is transported.

Waves are classified in different ways with their properties. For example, mechanical waves and electromagnetic waves are classified according to the medium they transport energy. Water waves and sound waves are examples of the mechanical wave, on the contrary, light waves, radio waves are examples of  electromagnetic waves. Electromagnetic waves can propagate in a vacuum but mechanical waves need a medium to transport energy.

Waves can propagate in 1D, 2D and 3D. Spring waves are examples of 1D waves, water waves are examples of 2D waves and light and sound waves are examples of 3D waves.

We can categorize waves according to their propagation direction under two title; longitudinal waves and transverse waves.

Transverse Wave: In this types of waves, a direction of wave and motion of particles are perpendicular to each other. Picture given below shows this wave type.

Longitudinal Wave: In this type of waves, the direction of the particles and wave are same. Look at the given picture below.

Magnetism Cheatsheet

Magnetism Cheat Sheet

 Magnets exist always in dipoles North Pole (represented by N) and South Pole (represented by S). If you break the rock into pieces you get small magnets and each magnet also has two poles N and S.

Same poles of the magnet like in the electricity repel each other and opposite poles attract each other.

Coulomb’s Law for Magnetism

Magnets exert force to each other.

F1=-F2

Where; k is the constant, m1 and m2 are the magnetic intensities of the poles and d is the distance between them. 

Magnetic Field

Magnets show repulsion or attraction force around itself. This area affected from the force of magnets called magnetic field. Direction of the magnetic field lines shown below;

Magnetic field lines around a wire are shown below;   

Magnetic field is a vector quantity and showed with the letter B. Unit of B is Tesla. When we calculate magnetic field of a magnet we assume that there is a 1 unit of m at the point we want to find. We find the magnetic field with the following formula;

Magnetic Flux

Magnetic flux is the number of magnetic field lines passing through a surface placed in a magnetic field.

 We show magnetic flux with the Greek letter; Ф. We find it with the following formula;

Ф=B.A.cosӨ

Where Ф is the magnetic flux and unit of Ф is Weber (Wb)

B is the magnetic field and unit of B is Tesla

A is the area of the surface and unit of A is m2

Magnetic Permeability

Diamagnetic matters: If the relative permeability f the matter is a little bit lower than 1 then we say these matters are diamagnetic.

Paramagnetic matters: If the relative permeability of the matter is a little bit higher than 1 then we say these matters are paramagnetic.

Ferromagnetic matters: If the relative permeability of the matter is higher than 1 with respect to paramagnetic matters then we say these matters are ferromagnetic matters.

Magnetic Effect of Current

If you move the magnet placed near the circuit you produce current or, if you change the current of a circuit you can get current in another circuit placed near it.

Magnetic Field around a Wire

Current flowing in a linear wire produces magnetic field B=2k.i/d at a distance d.

We show the current in two ways, if the current towards to us we show it with a dot if the current is outward we show it with the cross.

Magnetic Field around a Circular Wire

Circular wire produces a magnetic field inside the circle and outside the circle. Magnetic field around a circular wire is calculated by the formula;

B=2πk.i/r

Magnetic Field around a Solenoid

Picture given below shows the solenoid. A typical solenoid behaves like a bar magnet. Magnetic field produced by a solenoid is constant inside the solenoid and parallel to the axis of it.

We find the magnetic field produced by solenoid with the following formula;

Where: i is the current, N is the number of loops and l is the length of the solenoid.

 Force Acting on Moving Particle and Current-Carrying Wire

Experiments were done on this subject show that we can find the force exerted on the current carrying wire with the following formula;

 F=B.i.l.sinß 

We find the direction of the force by right-hand rule. Picture given below shows the direction of magnetic field current and force;

 Force Acting on Charged Particle

If the particle has charge q, velocity v and it is placed in a magnetic field having strength B force acting on this particle and ß is the angle between the velocity and magnetic field is found with following formula;

F=q.v.B.sinß

Forces of Currents Carrying Wires on Each Other

Experiments done on this subject shows that currents in the same direction attract each other since they produce opposite magnetic fields. On the contrary currents in opposite directions repel each other since they produce magnetic fields having same directions. We find the force exerted on each of them with the following formula, 

Where; l is the length of the wires, d is the distance between them.

Transformers

Transformers are devices used for changing the potential of alternating currents. Structure of simple transformer is given below;

Voltage is applied to the primary coil and, we take transformed voltage from secondary coil. There are two types of the transformer, step up and step down. We use a step down transformers in electrical devices like radio, and step up transformers in the welding machine.

Step Up Transformer

This type of transformer used for increase the incident voltage. Number of turns in the secondary coil is larger than the number of turns in the primary coil.

Step Down Transformer

This type of transformer used for decrease incident voltage. Number of turns in the primary coil is larger than the number of turns in the secondary coil.

Transformer Equations

 Vp is the potential, Ip is the current, Np is the turn on the primary coil and  Vs is the potential, Is is the current, Ns is the turn on the secondary coil. We use following equations to find potential, current or number of turns of any coil;

N1/N2=V1/V2=I2/I1

Force Acting on Moving Particle and Current Carrying Wire

As we learned before, charged particles produce an electric field around themselves. In an electric field charged particles are exerted force F=qE. The motion of the charges in an electric field produce current and as a result, of the current magnetic field is produced.  This magnetic field exerts the force on the charged particles inside the field. Experiments were done on this subject show that we can find the force exerted on the current carrying wire with the following formula;

F=B.i.l.sinß 

where B is the magnetic field strength, i is the current and l is the length of the wire and ß is the angle between the magnetic field and the wire.

We find the direction of the force by right-hand rule. Picture given below shows the direction of magnetic field current and force;

If the angle between the current and magnetic field ß;

 1. ß=0 then sinß=0, F=0

 2. ß=180 then sinß=0, F=0

 3. ß=90 then sinß=1, F=B.i.l

We can say that, if the direction of a current and magnetic field are parallel to each other then, no force exerted on the wire.

Example: Which one of the magnetic force acting on the wires is/are zero given in the picture below?

Since the directions of the currents i1 and i2 are parallel to the direction of magnetic field, no force exerted on these currents. F1=F2=0

i3 current is perpendicular to the magnetic field thus,

F3=B.i3.l

 Direction of the magnetic force is toward us.

Example: Find the directions of the magnetic forces acting on the currents i1, i2 placed in a constant magnetic field.

Magnetic forces acting on the currents i1 and i2 are shown in the picture below.

 Force Acting on Charged Particle

 Force acting on a current is explained above. We have learned that current is produced by the motion of charged particles. Thus, the force on current carrying wire is the sum of forces acting on each charged particle which this current. If the particle has charge q, velocity v and it is placed in a magnetic field having strength B force acting on this particle and ß is the angle between the velocity and magnetic field is found with following formula;

F=q.v.B.sinß

If;

1. v=0, then F=0 no force exerted on the stationary particle in a magnetic field.

2. ß=0, then sin0=0 and F=0

3. ß=180, then sin180=0, and F=0, magnetic field lines and velocity of particle parallel to each other, then no force exerted on it.

4. ß=90, then sin90=1, F=q.v.B

Forces of Currents Carrying Wires on Each Other

Experiments done on this subject shows that currents in the same direction attract each other since they produce opposite magnetic fields. On the contrary currents in opposite directions repel each other since they produce magnetic fields having same directions. We find the force exerted on each of them with the following formula, 

Where; l is the length of the wires, d is the distance between them.

Magnetic Field Around Solenoid

Picture given below shows the solenoid. A typical solenoid behaves like a bar magnet. Magnetic field produced by the solenoid is constant inside the solenoid and parallel to the axis of it.

We find the magnetic field produced by solenoid with the following formula;

Where: i is the current, N is the number of loops and l is the length of the solenoid.

We find the direction of a magnetic field by using right-hand rule again. Grab the solenoid as your four fingers show the direction of current and your thumb shows the direction of magnetic field.

Example: Find the magnetic field produced by the solenoid if the number of loops is 400 and current passing through on it is 5 A.( Length of the solenoid is 40cm and k=10-7N/Amps2)

N=400, i=5A, l=40cm=0.4m, k=10-7N/Amps2,

Example: A solenoid has 80 cm diameter, the number of loops is 4 and magnetic field inside it is 1,2 .10-5N/Amp.m. Find the current passing through the each loop of wire.

Since the questions ask current on each loop, we assume each loop as circle thus we find the magnetic field;

Example: There are two solenoids given below, they have equal lengths and i1=4Amps and i2=3Amps.  Find the magnetic field vector at point A.

i1 current produces B1 magnetic field and i2 current produces B2 magnetic field. We sum these vectors using vector properties and get following total magnetic field vector at point A.

Magnetic Field Around Circular Wire

Magnetic Field around a Circular Wire

Circular wire produces magnetic field inside the circle and outside the circle. Magnetic field around a circular wire is calculated by the formula;

B=2πk.i/r

Direction of the magnetic field at the center of the circle is found with right hand rule.

Your thumb shows the direction of magnetic field and four fingers show direction of current. Moreover, we can show the direction of current inside the circle with following pictures;

Example: Find the magnitude and direction of magnetic field at the center of the semicircle given below.

When we apply right hand rule we see that direction of magnetic field is inward to the page as shown in the picture below, since we have semicircle, we put 1/2 in front of our formula;

 Example: Directions of i1 and i2 currents are opposite. If the magnetic field at the center of the circles is zero find the ratio of i1 to i2 i1/i2?

Smaller circle has magnetic field ;

  Example: Find the magnetic field produced by currents i1 and i2 at point O.

If we apply right hand rule, directions of currents are;

i1:inward

i2:outward

Thus, total magnetic field at point O becomes the difference of these magnetic fields.