**Magnetism and Matter Important Questions for CBSE Class 12 Physics Magnetic Dipole and Magnetic Field Lines**

1.The magnetic dipole moment of a magnetic dipole is given by M = mx 21

where, m is pole strength and 21 is dipole length directed from The SI unit of magnetic dipole moment is A-m^{2} or J/T. It is a vector quantity and its direction is from South pole to North pole.

2.**Coulomb’s Law in Magnetism** Magnitude of force acting between two magnetic poles is given by

where, m_{1} and m_{2} are magnetic strength of poles and k is magnetic force constant. Its SI unit is A-m.

3.**Magnetic Field Lines** These are imaginary lines which give pictorial representation for the magnetic field inside and around the magnet.

Their properties are given as below:

- These lines form continuous closed loops.
- The tangent to the field line gives direction of the field at that point.
- Larger the density of the lines, stronger will be the magnetic field.
- These lines do not intersect one another

5.**Torque** on a bar magnet in a uniform magnetic field is

6.**Potential energy** of a magnetic dipole in a magnetic field is given by

8.Current loop behaves like a magnetic dipole whose dipole moment is given by

M=IA

The direction of dipole moment can be obtained by right hand thumb rule. Its. SI unit is A-m^{2}.

9.Magnetic dipole moment of a revolving electron is given by

10.Interaction between two magnetic dipoles is

11. **Oscillation of a Freely Suspended Magnet** The oscillations of a freely suspended magnet (magnetic dipole) in a uniform magnetic field are SHM.

where, I – moment of inertia of the magnet, M = magnetic moment and B – magnetic field intensity.

12.**Bar Magnet as an Equivalent Solenoid** The expression of magnetic field at distance r from centre is given by

This expression is equivalent to that of bar magnet.

13.**The Electrostatic Analog**

The table given below summarises the analogy between electric and magnetic dipoles

14.**Magnetism and Gauss’ Law**

**Previous Years’ Examination Questions**

**2 Marks Questions**

**1.Draw the magnetic field lines due to a current passing through a long solenoid. Use Ampere’s circuital law, to obtain the expression for the magnetic field due to the current I in a long solenoid having n number of turns per unit length. [Delhi 2014c]**

Let a and b be two long straight parallel conductors. I_{a} and I_{b} are the current flowing through them and separated by a distance d. Magnetic field induction at a point P on a conductor b due to current I_{a} passing through a is

**2.(i) Two long straight parallel conductors a and b carrying steady currents I _{a} and I_{b }respectively are separated by a distance d. Write the magnitude and direction, what is the nature and magnitude of the force between the two conductors?**

**(ii) Show with the help of a diagram, how the force between the two conductors would change when the currents in them flow in the opposite directions. [Foreign 2014]**

Now, let the direction of current in conductor b be reversed. The magnetic field B_{2} at point P due to current I_{a} flowing through a will be downwards. Similarly, the magnetic field B_{:} at point Q due to current I_{b }passing through b will also be downward as shown. The force on a will be, therefore towards the left. Also, the force on b will be towards the right. Hence, the two conductors will repel each other as shown.

**3.A circular coil of N turns and radius R carries a current I. It is unwound and rewound to make another coil of radius R/2, current I remaining the same. Calculate the ratio of the magnetic moments of the new coil and the original coil. [All India 2012]**

**4.A circular coil of N turns and diameter d carries a current I. It is unwound and rewound to make another coil of diameter 2d, current I remaining the same. Calculate the ratio of the magnetic moments of the new coil and the original coil. [All India 2012]**

**5.Explain the following:**

**Why do magnetic lines of force form continuous closed loops?****Why are the field lines repelled (expelled) when a diamagnetic material is placed in an external uniform magnetic field? [Foreign 2011]**

**6.A small compass needle of magnetic moment M and moment of inertia I is free to oscillate in a magnetic field It is slightly disturbed from its equilibrium position and then released. Show that it executes simple harmonic motion. Hence, write the expression for its time period. [HOTS, Delhi 2011C]**

**7.How does a circular loop carrying current behaves as a magnet? [Delhi 2011]**

**Ans**.The current round in the face of the coil is in anti-clockwise direction, then this behaves like a North pole, whereas when it viewed from other sc le, then current round in it is in clockwise direction necessarily forming South pole of magnet.

Hence, current loop have both magnetic poles and therefore, behaves like a magnetic dipole

**8.Deduce the expression for the magnetic dipole moment of an electron orbiting around the central nucleus. [All India 2010, Foreign 2009]**

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