ANU UG/Degree 4th Sem(Y23) Electricity and Magnetism Unit Wise Important Questions are now available, these questions are very important for your semester exams. These questions are prepared by top qualified faculty. Read these questions for good marks.
Gauss’s law-Statement and its proof, Electric field intensity due to (i) uniformly charged solid sphere, Electrical potential–Equipotential surfaces, Potential due to a uniformly charged sphere. Dielectrics-Polar and Non-polar dielectrics- Effect of electric field on dielectrics, Dielectric strength, Electric displacement D, electric polarization Relation between D, E and P, Dielectric constant and electric susceptibility.
Short Answer Questions
- Define Gauss’s law and briefly discuss its physical significance in relating the electric flux through a closed surface to the enclosed charge.Using Gauss’s law, outline the steps required to derive the expression for the electric field at a point inside a uniformly charged solid sphere.
- What are equipotential surfaces? Describe their main properties and explain how they relate to electric field lines.
- How is the electric potential at a point calculated for a uniformly charged sphere? Summarize the method used for such a derivation.
- Define the electric displacement vector and explain its relation to the electric field and the polarization in a dielectric medium.
- Distinguish between polar and non-polar dielectrics. Provide one example for each type and mention one key property that differentiates them.
Long Answer Questions
- Provide a detailed proof of Gauss’s law starting from Coulomb’s law. Include the necessary symmetry arguments and integration over a closed surface to show how the total electric flux relates to the enclosed charge.
- Derive the expressions for the electric field intensity both inside and outside a uniformly charged solid sphere using Gauss’s law. Discuss the assumptions made, the role of symmetry, and the continuity of the field at the surface of the sphere.
- Discuss the concept of electric potential in detail. Explain how equipotential surfaces are defined and their relationship to the electric field. Include a diagram to illustrate how the electric field vectors intersect these surfaces perpendicularly and explain the implications of this relationship.
- Derive the expression for the electric potential both inside and outside a uniformly charged sphere. Explain how the potential is related to the electric field, and discuss any conditions (such as continuity at the boundary) that must be satisfied.
- Describe in detail how an external electric field affects dielectrics. Discuss the process of polarization, the concept of dielectric strength, and the factors that influence the response of both polar and non-polar dielectrics in an electric field.
- Analyze the relationship between the electric displacement , the electric field , and the polarization in dielectrics. Include the derivation of the relationand explain how the dielectric constant and electric susceptibility are defined and related to these quantities. Provide examples or scenarios where these relationships are applied.
UNIT-II Current electricity
Electrical conduction-drift velocity-current density, equation of continuity, ohms law and limitations, Kirchhoff’s Law’s, Wheatstone bridge-balancing condition - sensitivity. Branch current method, Nodal Analysis, star to delta & delta to star conversions. Superposition Theorem, Thevenin's Theorem, Norton's Theorem, Maximum power transfer theorem.
Short Answer Questions
- Define drift velocity and explain its relationship with current density in a conductor.
- What is the equation of continuity in the context of electrical conduction, and what does it signify about charge conservation in a circuit?
- State Ohm’s law and briefly discuss one or two scenarios or materials where Ohm’s law might not hold.
- Summarize Kirchhoff’s current and voltage laws and explain how they apply to the analysis of electrical circuits.
- What is the balancing condition for a Wheatstone bridge, and what is meant by its sensitivity?
- Explain the purpose of converting between star (Y) and delta (Δ) configurations in circuit analysis.
Long Answer Questions
- Provide a detailed explanation of electrical conduction, discussing drift velocity and current density. Derive the equation of continuity and explain how it ensures charge conservation in a circuit.
- Derive Ohm’s law starting from the microscopic view of charge carrier motion in a conductor. Discuss the underlying assumptions made during the derivation and provide examples where these assumptions break down.
- Present a detailed analysis of Kirchhoff’s current law (KCL) and voltage law (KVL). Explain their theoretical basis, derivation from conservation principles, and demonstrate their application with a worked-out example circuit.
- Discuss the working principle of the Wheatstone bridge. Derive the condition for a balanced bridge and explain the concept of sensitivity in a Wheatstone bridge.
- Compare and contrast the branch current method with nodal analysis. Explain how each method is implemented, outline their advantages, and solve a sample circuit using one of these methods.
- Provide an in-depth discussion of Thevenin’s and Norton’s theorems. Derive their equivalent circuits, explain their practical uses, and derive the maximum power transfer theorem with an illustrative example.
UNIT-III Magneto statics
Biot-Savart’s law and its applications: (i) circular loop and (ii) solenoid, Ampere’s Circuital Law and its application to Solenoid, Hall effect, determination of Hall coefficient and applications.
Short Answer Questions
- State Biot-Savart’s law and briefly explain its significance in determining magnetic fields due to current elements.
- Using Biot-Savart’s law, derive the expression for the magnetic field at the center of a circular current loop.
- Explain Ampere’s Circuital Law and its application in finding the magnetic field inside a solenoid.
- What is the Hall effect? Describe how it is used to determine the Hall coefficient.
- List two practical applications of the Hall effect in technology or instrumentation.
- Compare the magnetic field distributions produced by a circular loop and a solenoid based on Biot-Savart’s law and Ampere’s law, respectively.
Long Answer Questions
- Derive the magnetic field at the center of a circular current loop using Biot-Savart’s law, detailing all steps and assumptions involved.
- Provide a detailed derivation of the magnetic field inside a long solenoid using Ampere’s Circuital Law, and discuss the conditions for its validity.
- Compare and contrast Biot-Savart’s law and Ampere’s Circuital Law in terms of their derivations, applications, and limitations in magnetostatics.
- Explain the Hall effect in depth, including the derivation of the Hall voltage in a current-carrying conductor placed in a perpendicular magnetic field.
- Discuss the experimental setup and procedure for determining the Hall coefficient of a material, highlighting the theoretical and practical challenges.
- Analyze the role of the Hall effect in modern sensor technology by discussing its principles, applications, and advantages over other magnetic field measurement techniques.
Electromagnetic Induction:
Faraday’s laws of electromagnetic induction, Lenz’s law, Self-induction and Mutual induction, Self-inductance of a long solenoid, Magnetic Energy density. Mutual inductance of a pair of coils. Coefficient of Coupling
Short Answer Questions
- Define Faraday’s law of electromagnetic induction and state its mathematical expression.
- State Lenz’s law and explain its significance in determining the direction of induced emf.
- What is self-induction? Briefly describe its principle with an example.
- Write the expression for the self-inductance of a long solenoid and mention the key parameters it depends on.
- Define mutual induction between two coils and explain how it is measured.
- What is the coefficient of coupling between two coils and how does it affect their mutual inductance?
Long Answer Questions
- Derive Faraday’s law of electromagnetic induction, explaining each step in the process, and discuss the physical significance of the induced emf.
- Explain Lenz’s law in detail, including its derivation and implications for energy conservation in electromagnetic systems.
- Compare and contrast self-induction and mutual induction, providing detailed derivations and examples for both phenomena.
- Derive the formula for the self-inductance of a long solenoid, and discuss the assumptions and conditions under which this expression is valid.
- Discuss the concept of magnetic energy density. Derive the formula for the energy stored in a magnetic field and explain its physical meaning.
- Derive the expression for the mutual inductance of a pair of coils and explain the factors that determine the coefficient of coupling between them.
UNIT-IV Electromagnetic waves-Maxwell’s equations:
Basic laws of electricity and magnetism- Maxwell’s equations- integral and differential forms Derivation, concept of displacement current. Plane electromagnetic wave equation, Hertz experiment-Transverse nature of electromagnetic waves. Electromagnetic wave equation in conducting media. Pointing vector and propagation of electromagnetic waves
Short Answer Questions
- State Maxwell’s equations in their integral form and briefly explain the physical meaning of each equation.
- Write Maxwell’s equations in differential form and discuss the significance of expressing them in this way.
- Explain the concept of displacement current and its role in modifying Ampere’s law.
- Write the equation for a plane electromagnetic wave in free space and state the conditions under which it is valid.
- Describe the key aspects of Hertz’s experiment and explain how it demonstrated the transverse nature of electromagnetic waves.
- Define the Poynting vector and explain its importance in describing the energy propagation of electromagnetic waves.
Long Answer Questions
- Derive Maxwell’s equations starting from the basic laws of electricity and magnetism, and show how the concept of displacement current is introduced to complete Ampere’s law.
- Starting from Maxwell’s equations in free space, derive the plane electromagnetic wave equation and discuss the significance of the wave speed in vacuum.
- Provide a detailed analysis of Hertz’s experiment, including the experimental setup, observations, and conclusions drawn about the transverse nature of electromagnetic waves.
- Derive the electromagnetic wave equation for a conducting medium, and discuss how conductivity influences wave propagation and attenuation.
- Explain the derivation of the Poynting vector from Maxwell’s equations and discuss its physical interpretation in terms of energy flow in electromagnetic waves.
- Compare and contrast the integral and differential forms of Maxwell’s equations, highlighting their interconnections and illustrating their application in solving electromagnetic problems.
UNIT-V Varying and alternating currents:
Growth and decay of currents in LR, CR, LCR circuits-Critical damping. Alternating current - A.C. fundamentals, and A.C through pure R, L and C. Relation between current and voltage in LR and CR circuits, Phasor and Vector diagrams, LCR series and parallel resonant circuit, Q –factor, Power in ac circuits, Power factor.
Short Answer Questions
- Define the time constant in an LR circuit and explain its role in the growth and decay of current.
- What is critical damping in an LCR circuit and how does it affect the circuit’s transient response?
- Describe the phase relationship between voltage and current in pure R, L, and C circuits when subjected to an alternating current.
- Explain the relationship between current and voltage in LR and CR circuits under AC conditions.
- What is a phasor diagram, and how is it used to represent AC quantities such as current and voltage?
- Define the Q-factor in the context of LCR circuits and discuss its significance in resonance phenomena.
Long Answer Questions
- Derive the equations describing the growth and decay of current in an LR circuit and a CR circuit, and explain the significance of the respective time constants.
- Provide a detailed analysis of an LCR circuit operating under critical damping conditions, including the derivation of the damping criteria and its implications on circuit behavior.
- Derive the mathematical relationship between current and voltage in an LR circuit under AC excitation, and illustrate your explanation with a phasor diagram.
- Discuss the behavior of alternating current in pure resistive, inductive, and capacitive circuits, highlighting the phase differences between current and voltage. Support your answer with relevant diagrams.
- Compare series and parallel LCR resonant circuits by deriving the resonance conditions for each configuration and analyzing the impact of the Q-factor on circuit performance.
- Explain the concepts of real power, reactive power, and apparent power in AC circuits. Derive the expression for power factor and discuss its significance in the efficient operation of AC systems.
