Magnetic Effects of Electric Current

Synopsis

Magnet and Electromagnet

• Magnetism is defined as the property of matter by which they can attract or repel each other because of electromagnetic force.
  Based on the magnetic property of a material, any material can be classified as
  
  
• Magnet: It is defined as the material that can produce an invisible magnetic field around them, because of which like poles attract each other and unlike poles repel each other.
  Types of magnetic material
  

Some important property of a magnet

1. Law of attraction: The strength of a permanent magnet is concentrated within a small region, which is at its end, as shown below. These regions of permanent magnets are known as poles of the magnet (i.e., North pole and South pole).
   
   
   
   
2. The polarity of magnet: When a magnet is freely suspended in air, it will try to align itself in a North-south direction because of the earth’s magnetic field.
3. Law of attraction or repulsion: Just like electric charges, like poles of a magnet always repel each other and unlike poles attract each other.
4. Magnetic poles: For any magnetic material, magnetic poles always exist in pairs also they will keep their property even after we break it into smaller pieces and will have two new north and south poles.
5. Magnetic induction: A magnet can induce its magnetic property to any magnetic material such that they also become permanent magnets under certain conditions.

Magnetic Field

Magnetic Field Lines: it is defined as the hypothetical curved lines that are drawn perpendicular to the surface of the magnet, which is used to describe the strength of a magnetic material and its magnetic property.

It is also known as magnetic lines of force.

Properties of the magnetic field line

1. Unlike electric lines of force, the magnetic field line always forms closed loops.
2. Magnetic field lines always move from the south pole toward the north pole of a magnet, whereas outside magnet field lines are directed away from the north pole and converge toward the south pole as shown below.
3. Magnetic lines of force do not intersect each other.
4. The direction of the magnetic field .at any instance is always perpendicular to the direction of magnetic lines of force.
5. The strength of the magnetic field is described as the number of lines of force passing through per unit area. (i.e., As we can see magnetic field strength is greater at its poles  since the number of magnetic field lines unit area is greater at its poles.)
   
   

Coulomb’s inverse square law

 

According to Coulomb’s inverse square law, the force of attraction or repulsion between two poles of the magnet is directly proposal to the product of their pole's strength and inversely proportional to the square of the distance between them.

Here, m₁ and m₂ are magnetic pole strengths of two magnets that are kept at a distance r from each other and K is proportionality constant .

For free space, the above equation can be expressed as,

 

Where μ₀ is the permeability of free space and has the value of 4π × 10^-7 henry. meter^-1

 

Magnetic field intensity (H): It is defined as the force experienced by a unit north pole of a magnet at any given point placed inside a magnetic field.

S.I unit of magnetic field intensity is ampere/ meter (A/m) and C.G.S unit is oersted.

Whereas the relation between magnetic flux density (B) and magnetic field intensity (H) is given as

B = μH

This relation shows that both B and H represent magnetic field at a certain point, the only difference is that magnetic field intensity (H) does not depend on the medium.

 

Magnetic moment (M): For a bar magnet the magnetic moment is defined as the product of its pole strength and length.

i.e., M = (2l) × m

The S.I unit of magnetic moment is the ampere meter square (A-m²).

Oersted's Experiment

In 1820 Hans Christian Oersted a Danish scientist who first discovered the relationship between electric current and magnetism.

According to his experiment, when a magnetic needle is bought near a current-carrying wire such that needle is placed just below the wire in a direction perpendicular to the axis of the magnetic needle as shown below

In this case, when the current starts flowing from north to south, the needle gets deflected toward easy. Similarly in case if current starts flowing from south to north, the needle will be deflected towards the west.

From this, we can make the following observation

1. A current-carrying wire can produce a magnetic field around it, and the intensity of the magnetic field is directly proportional to the intensity of the current flowing through the wire.
2. The magnetic field is produced in the direction perpendicular to the direction of current flowing through a wire.
3. The direction of the magnetic field and the direction of current flowing through a wire are related to each other.
   
   

 

Fleming’s Left-Hand Rule

According to Fleming’s left-hand rule the direction of a magnetic field, electric current, and force acting on a conductor will always be perpendicular to each other and they are represented by thumb, index finger, and middle finger respectively as shown in the figure below.

 

 

Note: For electric current, we use the left-hand rule, and for a moving electric charge or induced current we use the right-hand rule to describe the direction of force and the magnetic field associated with current and induced current/charge respectively.

 

 

Right-hand Thumb Rule

As we know a moving charge through a conductor can produce a magnetic field around itself, whereas the intensity and direction of the induced magnetic field will depend on the direction of current flowing through a conductor.

Based on this we can predict the direction of the magnetic field associated with a current-carrying conductor using the right-hand thumb rule. To understand this imagine you are holding a current-carrying conductor in your right hand such that the thumb is pointed in a direction of current and the wrapped fingers around the conductor will represent the direction of magnetic filled associated with a current-carrying conductor as shown in the figure below.

 

 

Maxwell’s Screw Rule

 

To understand this, imagine you have a right-handed screw that is rotating in an anticlockwise direction as shown in the figure below. From this, we can see that direction of current will be along the direction of advancement of the screw head.

 

 

 

Electric Motor

• Electric motor (D.C): it is a device that converts electrical energy to mechanical energy.
• The electric motor is used in every aspect of our daily and some of its applications are an electric fan, mobile fan, etc.
• And works on the principle of torque experienced by a current-carrying coil when placed in an external magnetic field.

The main components of the electric motor are

1. Rectangular coil: insulated copper wire bend in rectangular shape with sides ABCD.
2. Two permanent magnets: Permanent magnets are used to produce a constant magnetic field across the coil.
3. Brushes (X and Y): It connects power supply and
4. Switch key: When a key is closed the circuit is complete and current starts flowing through the coil.
5. DC power supply: It provides electrical energy.
6. Commutator or Split ring (P and Q): It is used to change the direction of electric current after half rotation of a coil.
   
   

 

Working:

• When a key is closed a current in the coil enters from the source battery through the conducting brush X and flows back to the battery through brush Y.
• As we can see, the current in the arms AB and CD will flow in opposite directions.
• On applying Fleming’s left-hand rule, we find that the force acting on the arm AB pushes it downwards while the force acting on the arm CD pushes it upwards.
• This produces a torque around the axle, such that in our case the coil and the axle rotate in the anti-clockwise direction and after half rotation, the current in the coil gets reversed with the help of a commutator.
• This reverses the direction of the force acting on the two arms AB and CD. However, these arms have reversed positions after that half rotation.
• Thus, the coil and the axle will keep on rotating in the same direction, in our case, it is anti-clockwise direction.
• Hence by applying electric current, we can produce mechanical work, and the speed of rotation can be changed by changing the electric current across the coil.

 

Faraday's Law of Electromagnetic Induction

Michael Faraday a British scientist performed a series of experiments to study the property of electromagnetic induction and finally, in 1831 he proposed the famous law of electromagnetic induction also known as the Faraday law of electromagnetic induction.

 

Based on his observation the law for electromagnetic induction can be given as

• Faraday’s first law of electromagnetic induction: It states that if there is a change in magnetic flux through a closed-loop conductor, this will be induced emf (Electromotive force or voltage) across the loop. The induced emf persists only as long as there is a change or cutting of flux.

• Faraday’s second law of electromagnetic induction: for a closed-loop conductor the induced emf is directly proportional to the rate of change of magnetic flux.
  
  

 

Lenz's law

According to Lenz law, the polarity of induced emf will be such that the induced current in a circuit will oppose the change in magnetic flux that produced it.

 

Lenz’s law is used to show the direction in which voltage is induced in a circuit. As we can see the negative shown the direction of induced emf caused because of the rate of change of magnetic flux.

 

 

Electric Generator

• Electric generator (A.C): it is based on the principle of electromagnetic induction and they convert mechanical energy into electrical energy. It is similar to an electric motor which converts electric energy to mechanical energy.
• An electric generator consists of a rotating rectangular coil placed between the two poles of a permanent magnet.
  
  

 

Working: 

• The two split rings P and B are fixed along the axle such that the current can easily flow through a rectangular coil ABCD inside the magnetic field when the axle is rotated about its axis.
• The outer ends of the two brushes B₁ and B₂ are connected to the galvanometer to measure the flow of current in the given external circuit.
• When the axle is rotated, arm AB moves upward and the arm CD moves downward in a constant magnetic field.
• In our case let's assume that the coil ABCD is rotated in the clockwise direction, thus by applying Fleming’s right-hand rule, the induced currents are set up in these arms along with the directions AB and CD. Thus, an induced current flow in the direction ABCD.
• If there are more turns in the coil, the current generated in each turn adds up to give a large current through the coil similarly by adding an iron core between the coil we can increase the amount of included current through the coil.
• After half rotation, CD and AB reverse direction, and thus, CD start moving up and AB starts moving down, now because of split-ring type commutator the direction of induced current produced along with AB and CD also get reversed.
• As a result of this, the direction of current induced across the will remain the same, unlike the A.C generator which uses a fixed ring attachment that produces an alternating current that changes its direction periodically.
• The difference between direct and alternating currents is that the direct current always flows in one direction, whereas the alternating current reverses its direction periodically.