Electrostatics Analogue of Magnetism

Potential Energy of a magnetic Dipole in a Magnetic Field

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 Field Strength at a Point Due to Bar Magnet

 

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.

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

  

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

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

5. 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.

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

3. 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.

4. 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.

5. 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.

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

  

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

8. 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.

9. 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.

  

10. 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.

11. 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.