## Saturday, January 12, 2013

### Torque on a Bar Magnet in a Magnetic Field

Let a bar magnet makes angle θ with magnetic field B and 2l be the length of the bar as show in figure.

Force on N-pole = mB along B and Force on S-pole = mB, opposite to B, since these are the equal and opposite forces they produce torque

ז = force x perpendicular distance. = mB x NA = mB x 2lsinθ therefore ז =MBsinθ

The direction of the torque is perpendicular to the the plain containing M and B, and given by right handed screw rules.

Magnetic dipole moment as the torque acting on a dipole held perpendicular to uniform magnetic field of unit strength

SI unit of M is JT-1

### Bar Magnet as an Equivalent Solenoid

To demonstrate the similarity of a current carrying solenoid to a bar magnet, let us calculate axial field of a finite solenoid carrying current.

Consider:           a = radius of solenoid
2l = length of solenoid with centre O
n = number of turns per unit length
I = current passing through solenoid
OP = r

Consider a small element of thickness dx of solenoid at distance x from O. and number of turns in element = n dx.
We know magnetic field due to n turns coil at axis of solenoid is given by

It is clear from the above expression that magnetic moment of a bar magnet is equal to the magnetic moment of an equivalent solenoid that produce the same magnetic field.

### Current Loop as a Magnetic Dipole

When we see a current carrying loop from top, current direction is anticlockwise and has north polarity. If, lower face of loop is seen from bottom then current direction is clockwise and have south polarity. Overall it behaves as a magnetic dipole depends upon

It is the magnetic moment of one turn loop of area one square metre carrying a current of one ampere.

NI factor is called as ampere turns of circular current loop

### Magnetic Dipole

Magnetic dipole consists to two unlike poles of equal strength and separated by a small distance.
The distance between the two poles of the bar is called magnetic length of the magnet. It is a vector directed from S-pole to N-Pole and represented by 2l.

Magnetic dipole is the product of the strength of either dipole (m) or the magnetic length (2l) of the magnet. It is represented by M.

It is vector quantity directed from South to North Poles.SI unit of M is ampere-meter2 or joule/tesla.

### Properties of Magnetic Field Lines

1. Magnetic field lines of a magnet form closed continuous loops. These lines are not discontinuous as of electric field.

1. Outside the body of magnetic direction of lines is from North Pole to South Pole.

1. Tangent to field line at any point gives the direction of magnetic field at that point.

1. Crowded lines represent a strong magnetic field and distant lines represent a weak magnetic field.

1. No two magnetic field lines can intersect the each other. Magnetic field cannot have two tangent directions at a same point on line.

### The Magnetic Field Lines

A space around a magnet or a conductor carrying current, in which force of attraction or repulsion on a magnet can be perceived is called magnetic field. Faraday introduces magnetic field line to visualize the existence of the lines.

According to the Faraday  magnetic field lines are the imaginary curve, tangent to which at any point gives the direction of magnetic field at that point. The path along with compass needle is aligned is known as the magnetic field lines.

### Some Basics of Magnetism

1. Earth behaves as a magnet: This is as if a big magnet is held at the center of the earth with its north pole pointing towards geographic South Pole and South Pole pointing geographical North as shown in the figure.

1. Every magnet attracts small pieces of iron, cobalt, nickel and steel towards it .The attraction is maximum at the two ends of a magnets.

1. When a magnet is suspended freely with the help of thread, it comes to rest along the north south direction. The pole of magnet which points towards geographic north is called North Pole and opposite end facing towards geographic south is call South Pole.

1. Poles exist in pairs; two poles of magnet are always of equal strength. The magnetic length of magnet is 6/7 of actual length of the magnet.

1. A straight line XX’ passing through the south and North Pole is called as axial line. And a line YY’ passing through the centre and perpendicular to length is called equatorial line.

1. A plane passing through N-S line of a freely suspended magnet is called magnetic meridian.

1. Like poles repel each other and unlike pole attract each other.

1. The force of attraction and repulsion F between two magnetic poles of strength m1 and m2 separated by a distance r is directly proportional to the product of poles strength and inversely proportional to the square of the distance between the centres.

Magnetic poles said to be one ampere-meter, if it repel s and equal and similar pole with a force of 10-7 N, when placed in vacuum at a distance of one meter.

1. The magnetic poles exist in pairs and do not exist in monopole. Each piece of a broken magnet is a complete magnet in itself. Isolated magnetic north and south poles are called monopoles and they do not exist.

1. When a piece of magnetic material is places near to a magnet, it acquires magnetism. The magnetism so acquired is called induce magnetism and the property of magnet is called inductive property.

1. Repulsion is sure test of magnetism. Two bar magnets repeals each other’s similar poles but they attract the iron piece with both the poles.

### Introduction

In nature an ore (Fe3O4) of the Iron attracts small pieces of irons towards it. This ore is called as magnetite. The phenomenon of attracting small bits of iron towards the ore is called magnetism.

The iron ore showing this effect is called a natural magnet. It is found that a piece of iron or steel can acquire magnetic properties, on rubbing with magnet. Such magnet made out of iron and steel are called artificial magnets.

A bar magnet is the most commonly used form of an artificial magnet. Two ends of the bar magnet are called poles of the magnet.

### Electromotive Force

Electromotive Force is the energy supplied by a source of electric power in driving a unit charge around the circuit. The unit is the volt. A difference in charge between two points in a material can be created by an external energy source such as a battery. This causes electrons to move so that there is an excess of electrons at one point and a deficiency of electrons at a second point. This difference in charge is stored as electrical potential energy known as emf. It is the emf that causes a current to flow through a circuit.

### Shunt

A shunt is a device which allows electric current to pass around another point in the circuit by creating a low resistance path.

## Friday, January 11, 2013

### Force on a Current Carrying Conductor Placed in a Magnetic Field

Force experienced by each electron in the conductor is

If n be the number density of electrons, A be the area of cross section of the conductor, then no. of electrons in the element dl is nAdl. Force experienced by the electrons in dl is

### Lorentz Force

A current carrying conductor placed in a magnetic field experiences a force which means that a moving charge in a magnetic field experiences force.

Special Cases:

i) If the charge is at rest, i.e. v = 0, then Fm = 0. So, a stationary charge in a magnetic field does
not experience any force.
ii) If θ = 0°or 180°i.e. if the charge moves parallel or anti-parallel to the direction of the magnetic
field, then Fm = 0.
iii) If θ = 90°i.e. if the charge moves perpendicular to the magnetic field, then the force is
maximum. Fm (max) = q v B

## Saturday, January 5, 2013

### Differences Between Biot Savart’s Law And Coulomb’s Law

1.       E is produced by a scalar source (q) where as B is produce by vector source  (Idl)

2.       E is acting along the displacement vector where as B acts perpendicular to Ixr.

3.       E is not depended of θ where as B depends upon θ.

### Similarity Between Biot Savart’s Law And Coulomb’s Law

1.       Field at any point vary inversely as the square of the distance

2.       Both obey superposition principle

3.       The magnetic fields linear in the source just as electric field