Emft 30 questions.pdf

# Classmate Notes ## Page 1 **b) Define electric dipole and dipole moment?** A) Electric dipole is defined as two point charges of equal magnitude and opposite sign, separated by a distance which is small compared to the distance of point P, at which we want to know the potential of electric field....

# Classmate Notes ## Page 1 **b) Define electric dipole and dipole moment?** A) Electric dipole is defined as two point charges of equal magnitude and opposite sign, separated by a distance which is small compared to the distance of point P, at which we want to know the potential of electric field. $P = Qd$ e-m **c) Describe about energy density in a static electric field?** A) Energy density: The energy density within the volume is work done per volume and is denoted by "Wed". $Wed = \frac{dwe}{dv}$ The energy stored in joules $We = \frac{1}{2} (\epsilon_{o}E^{2}) dv$. Differentiate with respect to "v". $dwe = \frac{1}{2}(\epsilon_{o}E^{2})dv$ The energy density is given by $Wed = \frac{1}{2}(\epsilon_{o}E^{2})$ $D = \epsilon_{o}E$ $Wed = \frac{1}{2\epsilon_{o}} (D\epsilon_{o}E)$ $Wed = \frac{1}{2\epsilon_{o}} (D^{2})$ $D = \epsilon_{o}E$ $Wed = \frac{1}{2\epsilon_{o}} (D^{2})$ $ |E| = \frac{|D|}{\epsilon_{o}}$ => $Wed = \frac{1}{2\epsilon_{o}} (|D|^{2})$ ## Page 2 **What is Polarization?** The Polarization (P) is defined as the dipole moment per unit volume of the dielectric; $P = \frac{1}{\triangle V} \sum_{i=1}^{n} Q_{i} \triangle x_{i}$ **Write the statement of Biot-Savart's Law?** The Biot - Savart's law states that the magnetic field intensity produced by differential current element Idl is: $dH = \frac{Idl sin \theta}{4\pi |R|^{3}}$ $ H = \int_{L} \frac{Idl \times R}{4\pi |R|^{3}}$ **State Stokes' Theorem?** Stokes' Theorem states that the circulation of a vector field A around a (closed) path I is equal to the surface integral of the curl of A over the open surface S bounded by L provided that A and curl of A are continuous on S. $\int_{L} A.dl = \oint_{S} (\nabla \times A).dS = \int_{S} curl A.dS$ **Define self & mutual inductances?** **Self-inductance:** Self-inductance is a property of a coil or circuit that quantities its ability to induce an electromotive force itself, when the current flowing through it changes. The charging magnetic field induces an EMF that opposes the change in current according to Lenz's law. $L =\frac{N\phi}{I}$ **Mutual-inductance:** It describes the ability of one coil to induce an EMF in another nearby coil when the current in the first coil changes. This interaction occurs due to the magnetic field produced by the first coil and second coil. $M= \frac{N_{2}\phi_{21}}{I_{1}}$ ## Page 3 **Where:** * N is the number of turns in the coil. * $\phi$ is the magnetic flux linked with the coil. * I is the current flowing through the coil. * $N_{2}$ is the number of turns in second coil. * $\phi_{21}$ is the magnetic flux linked with coil due to current $I_{1}$ in the first coil. **What's Vector Magnetic Potential?** If vector magnetic potential is the vector field used in electromagnetism, postulating in the study of magnetic fields. It is denoted by "A" and is related to the magnetic field "B" through the following: $B = \nabla \times A$ **State Faraday's Laws of electromagnetic induction?** It states that electromotive force (EMF) induced in a closed circuit is directly proportional to the rate of change of magnetic flux through the circuit. It can be expressed as: $E = - \frac{d\phi_{B}}{dt}$ **Where:** * E is the induced EMF. * $\phi_{B}$ is the magnetic flux. * $\frac{d\phi_{B}}{dt}$ is the rate of change of magnetic flux. **Define Intrinsic Impedance?** It is known as characteristic impedance, and it refers to the ratio of electric field (E) to magnetic field H given medium. In electromagnetic wave propagation. It's a property of how an electromagnetic wave travels. $Intrinsic \ Impedance = Z =\frac{E}{H}$ * Permeability ($\mu$) $= Z = \sqrt{\frac{\mu}{\epsilon}}$ * Permittivity($\epsilon$)= $Z = \sqrt{\frac{\mu}{\epsilon}}$ ## Page 4 **State Gauss Law and its limitations?** The total electric flux $\phi$ passing through the surface is equal to the total charge enclosed by total surface. $\phi = Q_{encl}$ $\phi = \oint \epsilon_{o}\textbf{E}.d\textbf{s}$ $\phi = \oint \epsilon_{o}\textbf{E}.d\textbf{s} = \oint \epsilon_{o}(\nabla.\textbf{E})dv$ According to divergence theorem: $\oint \textbf{D}.d\textbf{s} = \int_{v} (\nabla.\textbf{D})dv$ $\oint \textbf{D}.d\textbf{s} = \int_{v} (\rho) dv = Q_{encl}$ $(\nabla.\textbf{D})dv = \rho dv$ **Limitations:** * It cannot be applied if charge distribution are not symmetric. * It can be applied only for a closed surface, that Gausian surface for. **State Ampere's Circuital Law?** This law states that "the line integral of tangential component of magnetic field intensity (H) around a closed path is equal to total current I enclosed by that path". $\oint \textbf{H}.d\textbf{l} = I_{enc}$ $\nabla\times\textbf{H} = \textbf{J}$ ## Page 5 **List boundary conditions for two dielectric medium?** When dealing with the interface between two dielectric media, there are several important boundary conditions that describe how electric field (E), magnetic fields (H), electric displacement fields (D), and magnetic induction field (B) behave at the boundary. **1). Continuity of the electric field: (Tangential Component):** The tangential components of the electric field must be continuous across the boundary. $E_{1t} = E_{2t}$ Here $E_{1t}, E_{2t}$ are tangential components of electric fields in medium 1 and medium 2. **2). Continuity of the electric displacement field (Normal Component):** The normal component of the electric displacement field must satisfy; $D_{in} - D_{on} = \sigma_{s}$ Here $D_{in}, D_{on}$ are normal components on the electric displacement fields, and $\sigma_{s}$ is the free surface charge density. **3). Continuity of Magnetic field (Tangential Component):** The tangential component of the magnetic field must be continuous. $H_{1t}= H_{2t}$ **4). Continuity of The Magnetic Induction Field: (Normal Component):** The normal component of the magnetic induction field must satisfy: $B_{in} - B_{on} = 0$ ## Page 6 **Write the expression for the force on a moving charge?** The force on a moving charge q in an electromagnetic field is given by the Lorentz force Law, which combines the effects of electric and magnetic field: $F = q(\textbf{E}+\textbf{v} \times \textbf{B})$ **Where:** * F is the force on the charge. * q is the charge in Coulombs. * E is the electric field in Volts per meter (V/m). * v is the velocity of charge (in m/s). * B is the magnetic field (Tesla = T). * $\times$ is the cross product. **What is Magnetic scalar potential?** **Magnetic scalar potential** ($\phi_{m}$): In scalar quantity used in magnetostatics to describe static magnetic fields. It's defined such that: $B = -\nabla \phi_{m}$ * Notation 1: $\nabla \times B = 0$ (Curl of magnetic field is zero). * Relation: In magnetized materials, $B = \mu_{o}H + \mu_{o}M$. **Differentiate self and mutual inductance?** **Self-inductance:** **Definition:** Self-inductance is the property of a single coil that quantifies how much electromotive force is induced in itself due to the change in own current. **Formula:** $L = \frac{N\phi}{I}$ **Mutual-inductance:** **Definition:** Mutual inductance is the property of two coils that describes how much EMF is induced in one coil due to a change in another coil. **Formula:** The mutual inductance is: $M= \frac{N_{2}\phi_{21}}{I_{1}}$ ## Page 7 * Its units is Henry's (H). * Its applications are important in appliances where a single coil is used, like transformers and inductors. * Its units are Henry's (H). * Its applications are crucial in transformers designed in circuits where multiple inductors are coupled. **State Faraday's law of electromagnetic induction?** Faraday's law of electromagnetic induction states that the electromotive force (EMF) induced in a closed circuit is directly proportional to the rate of change of magnetic flux through the circuit. $E = -\frac{d\phi_{B}}{dt}$ **Where:** * E is the induced EMF. * $\phi_{B}$ is the magnetic flux. * $\frac{d\phi_{B}}{dt}$ is the rate of change of magnetic flux. ## Page 8 **State the formula for velocity of a uniform plane wave and what's the velocity of a uniform plane wave in free space?** The formula for the velocity (v) of a uniform plane wave in a medium is given by: $V = \frac{1}{\sqrt{\mu \epsilon}}$ **Where:** * $\mu$ is permeability of medium. * $\epsilon$ is the permittivity of the medium. **Velocity in free space:** In free space, the values for permeability and permittivity are: * $\mu_{0} = 4\pi \times10^{-7} H/m$ (Permeability of free space) * $\epsilon_{0} = 8.85 \times 10^{-12} F/m$ (Permittivity of free space). Then: $V = \frac{1}{\sqrt{\mu_{o} \epsilon_{o}}} \approx 3\times 10^{8} m/s$ Thus, the velocity of a uniform plane wave in free space is approximately $3\times 10^{8}$ meters per second, the speed of light. ## Page 9 **Define dipole and write the torque equation due to dipole?** **Def:** A dipole typically refers to a pair of equal and opposite charges or magnetic poles separated by a small distance. In the context of electric dipoles, it consists of two charges (+q and -q) separated a distance d. The dipole moment (P) is defined as: $P = qd$ **Where:** * q is the magnitude of one of the charges. * d is a vector pointing from the negative charge to the positive charge. It represents a small loop of current of two equal and opposite magnetic poles. **Torque equation for a dipole:** When placed in an external electric field (E) an electric dipole experiences a torque (T) given by the equation: $T = P \times E $ **Where:** * T is the torque * P is the dipole moment vector. * E is the external electric field. * $\times$ is the cross product. The magnitude of torque can be calculated as: $|T| = |P||E| sin \theta$ ## Page 10 **Describe briefly about Ohm's law?** Ohm's law is a fundamental principle in electrical engineering and physics that relates the voltage (V) and current (I) and resistance (R) in an electrical circuit. It states that the current flowing through a conductor between two points is directly proportional to voltage across the two points and inversely proportional to the resistance of the conductor. $V = IR$ **Where:** * V is the voltage. * I is the current. * R is the resistance. **Define polar molecules with an example?** **Polar molecules:** If polar molecules have a net dipole moment due to unequal sharing of electrons, resulting in partial positive and negative charges. **Characteristics:** * Unequal electron distribution: Caused by polar bonds. * Asymmetrical shape: Leads to an overall dipole moment. **Ex:** * **Water (H₂O):** * Bent shape, Oxygen is more electronegative. * High surface tension and solvent properties. * **Ammonia (NH₃):** * Trigonal pyramidal shape, Nitrogen is more electronegative. ## Page 11 **Describe the right-hand screw law?** The right-hand screw rule is a mnemonic used in physics and engineering to determine the direction of rotational motion or the relationship between vector quantities, particularly in electromagnetism. **To apply the right-hand screw rule:** * **Right Hand Orientation:** Extend your right hand. * **Screw motion:** Curl your fingers in the direction of the rotation or the direction of the current (electromagnetism). * **Thumb direction:** Your thumb will be pointing in the direction of the vector quantity you are interested in, such as the magnetic field (B) for a current-carrying wire. **Define vector magnetic potential?** **Vector Magnetic Potential:** Vector magnetic potential (A) is a vector field used in electromagnetism to describe the magnetic field (B) indirectly. It is practically useful in the analysis of magnetic fields produced by steady currents. **Def:** The vector magnetic potential is defined such that the magnetic field can be derived from it as follows: $B = \nabla \times A$ ## Page 12 **What is Toroid?** A toroid is a three-dimensional geometric shape that resembles a doughnut or ring. It is defined as a surface of revolution generated by rotating a circle around an axis that is in the same plane as the circle but does not intersect it. **Characteristics of Toroid:** * **Shape:** The basic shape is a hollow ring with a central hole. * **Dimensions:** It has a major radius and a minor radius. * **Applications:** * Commonly used in electromagnetism and electrical engineering. * In practice, in the design of inductors, transformers. **What's dynamically induced EMF?** Dynamically induced EMF refers to the electromotive force (EMF) generated in a conductor or coil due to a change in magnetic flux over time. This phenomenon is a consequence of Faraday's law of electromagnetic induction. It states that an EMF is induced in a closed circuit when the magnetic flux linking that circuit changes. **Cause:** Dynamically induced EMF occurs when either the magnetic field around the conductor changes or the conductor itself moves through a magnetic field. **Formula:** The induced EMF (E) can be expressed as: $E = -\frac{d\phi_{B}}{dt}$ **Where** $\phi_{B}$ is the magnetic flux. ## Page 13 **Write short notes on Skin Depth?** **Def:** Skin depth is a measure of how deeply an alternating current (AC) penetrates into a conductor. It is defined as the distance from the surface of the conductor at which the current density falls to 1/e (about 37%) of its value at the surface. **Formula** The skin depth (δ) can be calculated using the formula: $\delta = \sqrt{\frac{2\rho}{\omega \mu}}$ **Where:** * $\rho$ is the resistivity of the material. * $\omega$ is the angular frequency of the AC. * $\mu$ is the permeability of the material. **Write four applications of Poisson's equation, Laplace equation?** * **Electrostatics:** Electric potential, capacitors, conductors. * **Fluid Mechanics:** Incompressible flow. * **Gravity:** Gravitational potential. * **Image Processing:** Surface Reconstruction ## Page 14 **Laplace Equation:** * **Electrostatics:** Electric potential in charge-free regions. * **Fluid Mechanics:** Incompressible, irrotational flow. * **Heat Transfer:** Steady-state heat condition. * **Gravity:** Gravitational potential in mass-free regions. **Define magnetic flux and magnetic flux density?** **Magnetic flux** ($\phi$) is a measure of the amount of magnetic field passing through a given surface. It is a scalar quantity as well as the area and orientation of the surface. **Formula:** Magnetic Flux ($\phi$) = B.A. Its SI unit magnetic flux is Webers (Wb). **Magnetic flux density:** It is a vector quantity that describes the strength and direction of a magnetic field at a particular point. It is also known as magnetic field intensity or magnetic induction. **Formula:** Magnetic flux density (B) = $\phi$/A Its SI unit is Tesla (T).