MAGNETIC EFFECTS OF ELECTRIC CURRENT

Magnetic field due to charge flow:

When a magnetic needle is places near to the current carrying wire, it shows a deflection. This simple observation suggests that, a moving charge(in general current electricity) causes magnetic field.

If we observe the above figure, when the key is closed, the needle shows a deflection and when the circuit is open, there is no deflection. Hence

A charge in rest produces electric field A charge in motion produces electric field as well as magnetic field. Thus we can conclude that electricity and magnetism are linked to each other.

Origin of magnetic field:

We are studying the magnetic field and its properties since 600 B.C. A compass needle gets deflected when brought near a bar magnet. On a keen observation, one can find that the ends of the compass needle point approximately towards north and south directions of earth. The end pointing towards north is called north seeking or North Pole. The other end that points towards south is called south seeking or South Pole.

It is interesting to know, how actually the bar magnet North Pole is directed towards earth north pole. In the olden days it was think of a giant magnet present inside the earth, which is containing its South pole at the geographic North and its North pole at the geographic South; as shown in the figure.

But presently there are many hypothetical theories, which suggest that earth magnetic field is because of the molten metals present inside the earth core. This effect is called dynamo effect.

When we consider the earth magnetic field, the geographic North Pole acts like a south pole of magnet and geographic South Pole acts like a north pole of a magnet.The Earths magnetic north pole and South Pole are slightly away from its geographic North and South poles. This is shown below.

Magnetic field and field lines

The area around a bar magnet, in which it can show its influence is called magnetic field. The iron filings around a bar magnet will be arranged systematically due to influence of magnetic field. This is shown below.

If we bring a compass, the needle in the magnetic field will deflect. These

deflections will give the magnetic field directions. If we place a north pole of unit strength (isolated north pole never exists.) in a

magnetic field, it will be repelled by the north pole of magnet and will be attracted by the south pole.

The imaginary path of this north pole of unit strength is called as magnetic line of force

Properties of magnetic lines of force:

Magnetic field is a quantity that has both direction and magnitude. The direction of the magnetic field is taken to be the direction in which a north pole of the compass needle moves inside it.

Therefore it is taken by convention that the field lines emerge from north pole and merge at the south pole.

Inside the magnet, the direction of field lines is from its south pole to its north

pole. Thus the magnetic field lines are closed curves. The relative strength of the magnetic field is shown by the degree of closeness of

the field lines. The field is stronger, that is, the force acting on the pole of another magnet placed is greater where the field lines are crowded.

No two field-lines are found to cross each other. If they did, it would mean that at the point of intersection, the compass needle would point towards two directions, which is not possible.

Magnetic Force:

Let a moving charge q is with a velocity v in a magnetic field B. Then the force experienced by the charge is expressed as

( )F q v B

This force is called as magnetic force. It has the following properties

It depends on q, vand B(charge of the particle, the velocity and the magnetic field). Force on a negative charge is opposite to that on a positive charge.

The magnetic force q[ v B] includes a vector product of velocity and magnetic field. The vector product makes the force due to magnetic field vanish (become zero) if velocity and magnetic field are parallel or anti-parallel. The force acts in a (sideways) direction perpendicular to both the velocity and the magnetic field.

Its direction is given by the screw rule or right hand rule for vector (or cross) product.

The magnetic force is zero if charge is not moving (as then |v|= 0). Only a moving charge feels the magnetic force.

By applying the cross product rules, we have

sinF qvB n

Where is the angle between v and B.

Hence B, the magnetic field is defined as

sinFB

qv

i.e., the force experience by 1 C of charge, moving with a velocity 1m/s perpendicular to the magnetic field direction.

Units: Newton second / (coulomb metre). This unit is called as tesla (T). As tesla is very large unit, often gaussis used as a unit of magnetic field. 1 gauss = 10-4 T

Lorentz Force

As the magnetic field is created by the moving charge, we can assume two force.

Electrostatic force created by the charge, which is given by the expression,

F Eq

And the magnetic force created by the moving charge, which is given by the expression,

( )F q v B

By considering the above two forces, we have a combined force due to electric and magnetic fields, which is given by the expression

[ ( )]F q E v B

The above force is called as Lorentz force.

Magnetic Field Due To A Current-Carrying Conductor:

When a conductor is carrying current, a magnetic field will be generated in perpendicular direction. The compass needle shows different deflections, based on the direction of current.

The following two diagrams illustrate the situation of two possible current directions and corresponding compass needle deflection.

Magnetic Field due to a Current through a Straight Conductor

Consider a straight conductor carrying current. The magnetic field will be observed in the perpendicular direction of the wire. If we arrange iron filings on a sheet, they will be arranged as shown in figure. They form circular rings, concentric with wire and radially expanding.

The direction of the magnetic field is given by right hand thumb rule.

Right-Hand Thumb Rule:

A convenient way of finding the direction of magnetic field associated with a current-carrying conductor is discussed here.

Imagine that observer holding a current-carrying straight conductor in his right hand such that the thumb points towards the direction of current. Then his fingers will wrap around the conductor in the direction of the field lines of the magnetic field, as shown in figure.

Magnetic field Due To A current element:

(Biot Savart law)

Consider a current element dl from a current carrying conductor. To find the magnetic field due to this element, consider a point P at a distance of r from the element. Let be the angle between the radius vector r and the element dl.Let I be the current passing through the element.

The assumptions are shown in below figure.

Then the magnetic field at the point P is given by

|dB| = 04

. 2sinIdlr

This equation is called as Biot Savarts law and can be used for finding the magnetic field at a given point due to the current carrying conductor.

Here 0 is called as the permeability of free space (or vacuum). Its value is given by

0 = 4 x 10-7 Tm/A

Magnetic Field due to a Current through a Circular Loop

Consider a circular loop carrying current. Like straight conductor, this circular loop aso generates magnetic field perpendicular to current direction, everywhere on the circumference. This arrangement is shown below.

At every point of a current-carrying circular loop, the concentric circles representing the magnetic field around it would become larger and larger as we move away from the wire.

By the time one reach at the centre of the circular loop, the arcs of these big circles would appear as straight lines.

Every point on the wire carrying current would give rise to the magnetic field appearing as straight lines at the center of the loop.

By applying the right hand rule, it is easy to check that every section of the wire contributes to the magnetic field lines in the same direction within the loop.

We know that the magnetic field produced by a current-carrying wire at a given point depends directly on the current passing through it.

Therefore, if there is a circular coil having n turns, the field produced is n times as large as that produced by a single turn. This is because the current in each circular turn has the same direction, and the field due to each turn then just adds up.

By applying the BiotSavarts law, the amount of magnetic field at the far axial point of the circular loop is given by

B = 0 2

I iR

where I is the current passing through the loop

R is the radius of the circular loop

Magnetic Field due to a Current in a Solenoid

A coil of many circular turns of insulated copper wire (in general a conducting wire) wrappedclosely in the shape of a cylinder is called a solenoid.

The patternof the magnetic field lines around a current-carrying solenoid isshown in figure.

The magnetic field due to a solenoid is similar to the magnetic field generated by a bar

magnet. One end of the solenoidbehaves as a magnetic north pole, while the other behaves as

thesouth pole. The field lines inside the solenoid are in the form of parallel straight lines. This indicates

that the magnetic field isthe same at all points inside the solenoid. That is, the field isuniform inside the solenoid.

A strong magnetic field produced inside a solenoid can be used to magnetise a piece of magnetic material, like soft iron,when placed inside the coil. The magnet so formed iscalled an electromagnet.

The magnetic field generated by a solenoid due to current I is given by

B = 0nI where n number of turns per unit length.

Toroid:

The toroid is a hollow circular ring on which a large numberof turns of a wire are closely wound. It can be viewed as asolenoid which has been bent into a circular shape to close on itself.

The magnetic field due to a Toroid is given by

0

2NIBr

where N is the number of turns and r is the radius of toroid.

Force On A Current-Carrying Conductor In A Magnetic Field:

A conductor carrying current will generate a magnetic field. If this conductor is placed in an external magnetic field,it will experience force due to the external field. The force is given by

F BIl in magnitude.

where I is the current through the conductor

l is the length of the conductor;

B is the external magnetic field.

Due to this force, the conductor will displace from its original position. The direction of the force on the conductor depends upon thedirection of current and the

direction of the magnetic field. The displacement of the rod is largest when the direction of current is at right anglesto the

direction of the magnetic field.

Flemings left-hand rule:

According to this rule, stretch the thumb,forefinger and middle finger of your left handsuch that they are mutually perpendicular.If the first finger points in thedirection of magnetic field and the secondfinger in the direction of current, then the thumb will point in the direction of motion orthe force acting on the conductor.

Electric Motor:

An electric motor is a rotating device that converts electrical energy tomechanical energy.

An electric motor consists of a rectangularcoil ABCD of insulated copper wire as shown in figure.

The coil is placed between the two poles of a magnetic field such that the arm AB and CD are perpendicularto the direction of the magnetic field.

Theends of the coil are connected to the twohalves P and Q of a split ring.

The inner sides of these halves are insulated and attached to an axle. The external conducting edges ofP and Q touch two conducting stationarybrushes X and Y, respectively.

Current in the coil ABCD enters from thesource battery through conducting brushX and flows back to the battery through brush Y.

If we observe BC and AD carefully, the current will be parallel to the magnetic field direction and as a result, the force experienced by this part of the coil is zero.

On the other hand, current will be perpendicular to the magnetic field direction at AB and CD parts of the coil, which causes force on the conductor.

The force on AB and CD is exactly equal and opposite in direction and as a result a trque will be generated which causes rotations along the axis of the coil. This is illustrated in the following figure.

The torque acting on the coil is given by

IAB where I current through the coil A area of the loop B applied magnetic field.

Essential requirements of commercial electric motors:

An electromagnet in place of permanent magnet. Large number of turns of the conducting wire in the currentcarrying coil. A soft iron core on which the coil is wound.

Electromagnetic Induction:

A current-carrying conductor is placed in a magnetic field such that the direction of current is perpendicular to themagnetic field will experiences a force.

This force causes the conductor tomove. The same can be done in reverse. i.e, a moving magnet can be used to generate

electriccurrents.

If we move a magnet inside a solenoid. A deflection can be observed in the galvanometer, which indicates generation of currents.

Therefore we can conclude that electric and magnetic fields exists together but not separately.

The laws observed by Michael Faraday are the basic principles of electromagnetic induction and are used in many electronic applications like, electric motor, electric generator, dynamo, transformers etc.

ELECTRIC GENERATOR

Based on the phenomenon of electromagnetic induction, the experiments studied above generate induced current, which is usually very small. This principle is also employed to produce large currents for use in homesand industry.

In an electric generator, mechanical energy is used to rotatea conductor in a magnetic field to produce electricity.

An electric generator, as shown in figure, consists of a rotating rectangular coil ABCD placed between the two poles of a permanentmagnet.

The two ends of this coil are connected to the two rings R1and R2.The inner side of these

rings are made insulated. The two conducting stationary brushes B1and B2 are kept pressed separately on the rings

R1and R2, respectively. The two rings R1and R2are internally attached to anaxle. The axle may be mechanically rotated fromoutside to rotate the coil inside the magnetic

field. When the coil is rotating continuously, the magnetic lines force(field lines) will cut by

the coil and due to electromagnetic induction, a small current will be generated and can be observed in the galvanometer.

Here it should be noted that, increase in speed of mechanical rotations of coil will not increase the current generated.

Here the device is called as AC Generator. To get DC Voltages, a split-ring type commutator must be used.With this

arrangement,one brush is at all times in contact with the arm moving up in the field,while the other is in contact with the arm moving down.

DOMESTIC ELECTRIC CIRCUITS

The electricity supplied to the homes consists of two wires. Usually withred insulation cover, is called live wire (or positive). Another wire,

withblack insulation, is called neutral wire (or negative). In our country, thepotential difference between the two is 220 V.

These wires pass into an electricitymeter through a main fuse. Often, two separate circuits are used, one of 15 A current rating for appliances with

higher power ratings such as geysers, air coolers, etc. The other circuit is of 5 A current rating forbulbs, fans, etc.

The earth wire, which has insulation of green colour, isusually connected to a metal plate deep in the earth near the house.

This is used as a safety measure, especially for those appliances that have a metallic body, for example, electric press, toaster, table fan,refrigerator, etc.

The metallic body is connected to the earth wire, which provides a low-resistance conducting path for the current. Thus, it ensures that any leakage of current to the metallic body of the appliance keeps its potential to that of the earth, and the user may not get a severeelectric shock.

The general domestic wiring is shown below.

The wiring in home is usually parallel. Because, if we use series connections, if any

electronic device fails to work, the complete circuit breaks. To prevent this, parallel connections are used. In this even if a device fails to work, other devices will work.

Electric fuse:

Fuse is the most important safety device, used for protecting the circuits due toshort-circuiting or overloading of the circuits.

Overloading can occurwhen the live wire and the neutral wire come into direct contact. In such a situation, the current in the circuit abruptlyincreases. This is called short-

circuiting. The use of an electric fuse prevents the electric circuit and the appliance from a possible

damageby stopping the flow of unduly high electric current. The principle that fuses works is Joule heating. The Joule heatingthat takes place in

the fuse melts it to break the electric circuit. Overloading can also occur due to an accidental hike in the supplyvoltage.

Now days fuse is replaced with electric jumper which changes its position and stops electric flow during a short circuit.