Unit 04 Magnetic force in Electromagnetic field Theory Important Question AKTU Btech

Unit 04 in Electromagnetic Field Theory at AKTU Btech investigates Magnetic Force, including concepts, interactions, and technical applications such as motors, transformers, and sensors.

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Important Questions For Electromagnetic Field Theory:
*Unit-01     *Unit-02    
*Unit-03    *Unit-04 
*Unit-05    *Short-Q/Ans
*Question-Paper with solution 21-22 

Q1. A charged particle moves with a uniform velocity 4 m/s in x direction in a region where E = 20a_y Vhm and B = B₀a_z Wb/m² Determine B_o such that the velocity of the particle remains constant. 

Ans. 1. It follows that the particle’s acceleration is zero if it moves with a constant speed. In other words, there is no net force acting on the particle.  

Q2. A charged particle of mass 2 kg and charge 3 C starts at point (1, – 2, 0) with velocity 4 a_x +3a_z m/s in an electric field 12a_x + 10a_x Vim. At time t= 1 sec, determine the acceleration of the particle, its velocity, kinetic energy of the particles and its position.

Ans. 1. According to Newton’s second law of motion, 

2. Equating components and then integrating, we obtain 

7. Equating components yields

Q3. Write a short note on magnetic dipole.  

Ans. 1 Any magnetic dipole has a north pole and a south pole, which are two separate poles. Consequently, a basic bar magnet is referred to as a magnetic dipole. Every piece of this magnet, if broken into smaller parts, will form a dipole. 

2. Similarly, a small current carrying wire or loop is called as dipole, because it has the magnetic poles like bar magnet.  

3. Due to current carrying loop, the magnetic vector potential at point ‘P’ is

Q4. What is magnetic susceptibility? What is magnetization ?

Ans. A. Magnetic susceptibility: 

• 1. The magnetic dipoles contained in magnetic materials correlate to the atoms. We suppose that these magnetic dipoles are randomly orientated when at rest (initially). 
• 2. A magnetic field is produced by the electron’s rotation around its own axis, and magnetic dipole moments are also produced by the electron’s orbit around the positive nucleus.  
• 3. The magnetic dipoles inside a material are reoriented in accordance with the direction of the applied external magnetic field when an external magnetic field is applied to the material. 
• 4. The velocities of the circling electrons are impacted by the application of an external magnetic field. As a result, the atom acquires a tiny magnetic moment that, in accordance with Lenz’s rule, will work against the imposed magnetic field.
• 5. The measurement of this re-orientation is called magnetic susceptibility. This is denoted by the symbol X_m.
• 6. These materials fall into the category of paramagnetic materials. These components include iron, nickel, cobalt, etc.

B. Magnetization (M):

1. It is simply given as total magnetization, the values of this is given as the magnetic dipole moment per unit volume of a material in a volume ∇v. 

The quantity X_m is dimensionless and is called magnetic susceptibility of the medium. 

Q5. Write short notes on following : 

i. Inductor 

ii. Magnetic materials.

Ans. i. Inductor:

1. An inductor, also known as inductance, is a passive component that stores energy as a magnetic field. 

Example: Coil and solenoid. 

2. There are two types of inductances: 

A. Self inductance : A circuit’s self-inductance is a property that causes an e.m.f. to be generated within the circuit whenever the circuit current changes, opposing the current change.

We know that  

B. Mutual inductance:  

a. There are at least two circuits that have mutual inductance. Mutual inductance is what causes a circuit’s current to flow when the current in a nearby circuit changes.

3. Mutual inductance between circuit 2 and 1 is defined as flux linked with a circuit when a unit current flows in neighbouring circuit. 

i. Magnetic materials : There are three types of magnetic materials: 

1. Diamagnetic : A diamagnetic substance gets weakly magnetized in the direction perpendicular to the external magnetic field when exposed to a magnetic field. Diamagnetism is the name for this material characteristic. 

Examples: Bismuth, silver, copper and hydrogen.  

2. Paramagnetic: 

a. Magnetic dipoles are already present in paramagnetic materials. Although dipoles are randomly aligned and have a low net magnetic, these materials are permanently magnetized. 

b. The dipoles in these materials will point in the direction of the external magnetic field when they are exposed to it. Paramagnetism is a name for this characteristic.

Examples: Aluminium, platinum and oxygen. 

3. Ferromagnetic: When a ferromagnetic material is exposed to an external magnetic field, the magnetic lines of force are strongly drawn to it, and the domains then align themselves with the field’s direction to increase the flux generated by the external field. Ferromagnetism is the name for this characteristic. Examples: Iron, cobalt, nickel.

Q6. Prove the magnetostatic energy is given by

Ans. A. Energy stored in magnetic field:

1. When a current through an inductance coil is progressively increased from zero to the maximum value I, an inductor stores energy. 

2. The self-induced e.m.f. created by this change opposes the inductor’s energy change. This energy is kept in the coil’s magnetic field and later released when the field collapses.

B. Energy density in magnetic field: 

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