Phys 202 1nd Edition Lecture 24Outline of Last Lecture I. Example ProblemsOutline of Current Lecture II. Review of ConceptsA. Maxwell’s Equationsi. Coulomb’s Lawii. Gauss’s Lawiii. Kirchhoff’s Rulesiv. Biot-Savart’s Lawv. Ampere’s Lawvi. Snell’s RuleCurrent LectureReview of Concepts:Maxwells equations:Maxwells equations are a set of laws that describe how electric and magnetic fields are generated and altered by one another and by charges and currents.Coulomb’s law:Coulomb's law states that the electrical force(F) between two charged objects is directly proportional to the product of the quantity of charge on the objects(q1 and q2) and inversely proportional to the square of the distance(r) between the two objects. k in this equation is a proportionality constant (Coulomb's law constant). The value of k depends on the medium that the object is in, but for air it is equal to 9.0 x 109 Nm2/C2. This is represented by the equation; F=kq1q2/r2Gauss’s Law:Gauss’s law states that that the net electric flux(φ) through any closed surface is equal to the charge(Q) inside that surface divided by the permittivity (ε0). This is represented by the equation; φelectric=Q/εThese notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.Gauss’s law of magnetostatics:A magnet is surrounded by a magnetic field, very similar to how a charge is surrounded by an electric field. Magnetic field can be thought of as originating from the north pole and terminating at the south pole. This means that if you take a magnet, no matter how small, and surround it with a volume of any shape, for every magnetic field line that is leaving the object from the magnet, there is another magneticfield line moving in to the object and terminating at the magnet. Magnetic field is referred to as “B” and the unit is Tesla. The magnetic field of Earth(B) is roughly 10-5T.The amount of magnetic field lines, or magnetic flux, that moves through a surface is the surface integralof the normal component of the vector of magnetic field (B). This is described as;Φ=∫sB . dSWhich, since there is no such thing as an isolated monopole magnet, would be equal to zero. Because magnetic fields have no source or sinks and are magnetic field lines are continuous, we can also write this equation as;∮s❑B .dS=∮∇ BvS=0This is known as Gauss’s law of magnetostatics.Kirchhoff’s Rules:Kirchhoff’s rules describe several equalities dealing with current and voltage through a circuit. Kirchhoff’sfirst law, which is also sometimes called the “node rule”, states that at any node or point in an electrical circuit, the sum of currents flowing into that node is equal to the sum of currents flowing out of that node. Essentially, this means that the current coming in to a system must be equal to the current coming out of the system. Kirchhoff’s second rule is called the voltage rule, or sometimes the loop rule. This rule states that the sum of the potential differences (V) around any closed loop is equal to zero.Biot-Savart Law:Current gives rise to the B field. The Biot-Savart Law relates a magnetic field to the current that it comes from in a similar way that Coulomb's law relates an electric fields to the point charge that it comes from. Consider an electric wire with a length L carrying a current I. A magnetic field of magnitude B emanates from this wire out to a distance r from the wire. The equation for the magnitude of the magnetic field around this wire is;ΔB=(µo/4πr)i(ΔLrsin(θ)/r3) = (µ0/4π)(iΔl/r2)sin(θ)µo in this equation is a fundamental magnetic constant which is equal to 4πx10-7Ampere’s law:Ampere’s law states that the integral of B around any closed mathematical path equals µ0 times the current intercepted by the area spanning the path. In other words, if you add up the magnetic field at each point along a certain path encircling your current-carrying wire, then it will equal the amount of current enclosed by this path. Ampere’s law is represented by the equation: ∫B ∙ ∆ L=μ0ISnell’s law:Sometimes, when light enters a medium other than air, the path of the light is refracted, meaning that the path of the light changes by some degree, depending on the medium it enters. Light refracts throughdifferent mediums because the speed of light is different through different mediums (as opposed to the constant through a vacuum or air). Light will take whichever path from point a to point b that takes the least amount of time. The refraction angle of light can be measured using Snell’s rule, which is nsin(θi)=n2sin(θ2) Where θi is the angle at which the light hits the medium and θ2 is the angle of the refracted light throughthe medium. n defines the medium that light travels through (like water) and is equal to the velocity of light in the vacuum over the velocity of light. Because n of a vacuum (or air) is 1, n is always greater than or equal to one. For example, the n of water is equal to 1.33, n of glass is equal to 1.78, and n of diamond is about 4. n is the index of