Questions - Answers

In this chapter, we will study the effect of magnetic field on moving charges, how the particles can be accelerated to very high energies in cyclotron and how currents and voltages are detected by a galvanometer. Based on BIE model paper this chapter has a weightage of (2 + 8) marks, (2 + 4 + 4) marks.

2 Marks Questions

1. State Ampere's law and Biot-Savart law.
A: Ampere's Law: Total magnetic flux coming out of a current carrying conductor enclosed in a perpendicular plane is μ₀ times the algebraic sum of currents enclosed by all the conductors in that plane.

                                                
Biot - Savart's Law: Magnetic induction (dB) at a point due to an element of current at any point 'r' from the conductor is

2. A circular coil of radius 'r' having N turns carries a current i. What is its magnetic moment?
A: Magnetic induction at the centre of the coil

 
                  
                   
M is called Magnetic moment
 

3. What is the force on a conductor of length L, carrying current i placed in a magnetic field of induction B? When does it becomes maximum?
A: Force on a conductor in a magnetic field is F = Bil sinθ
θ is angle between length of the conductor (L) and magnetic field direction (). Force is maximum when θ = 90º. i.e. Fmax = Bil
 

4. A current carrying circular loop is placed in a uniform external magnetic field, if the loop is free to turn, what is its orientation when it achieves stable equilibrium?
A: The loop achieves stable equilibrium when torque τ = 0. i.e.

 
Magnetic moment (M) and magnetic field (B) are parallel to each other, then loop exists in stable equilibrium.
 

4 Marks Questions

1. Derive an expression for the magnetic induction at a point on the axis of a current carrying circular coil using Biot - Savart's law.
A: Let us consider a circular loop of radius R carrying a current I. Let P is a point on its axis at a distance of x from centre 'O'. The magnetic induction at 'P' due to an element 'dl' at a distance of 'r' from P is

2. Obtain an expression for the magnetic dipolemoment of a current loop.
A: Let us consider a rectangular loop of length 'b', breadth 'a', is placed in a uniform magnetic field B. 'θ' is the angle between field and normal to the loop. Forces on lengths of loop are F₁ and F₂.
F₁ = F₂ = BIb
Current passes through loop in opposite direction. So, F₁ and F₂ forms a couple. Total moment of couple

   
Compare it with    in case of electric dipole, then magnetic moment of current loop is M = I A for one turn For 'n' turns  
 

Direction of this magnetic moment is into the plane of the paper.

4. Distinguish between Ammeter and Voltmeter.
A: