Explain the physical meaning of each of the four Maxwell's Equations.
Gauss' Law for Electricity states that the electrical flux, the number of electrical field lines piercing an area, through a closed surface is proportional to the amount of electrical charge contained within the closed surface. Gauss' Law for Magnetism states that the magnetic flux, the number of magnetic field lines piercing an area, through a closed surface is zero, meaning that there are no magnetic monopoles. Faraday's Law of Induction, in conjunction with Lenz's Law, states that the line integral of the electric field around a closed loop is equal to the negative change in magnetic flux with respect to time, which creates an induced emf in the loop. Ampere's Law states that the line integral of the magnetic field around a closed loop is proportional to the sum of the current piercing the enclosed loop's area and the change in electric flux through the area with respect to time.
State one advantage and disadvantage of using the for-each loop when working with an array.
The for-each loop allows for a cleaner, more intuitive code when accessing the value or object associated with each array element. However, the for-each loop's syntax does not allow the programmer to change an array element's data. Instead, a simple for loop is preferred if the array elements' data need to be changed.
In addition to the Cartesian coordinate system, what are the two common coordinate systems that are used in Calculus III, and why is converting the coordinate system to either of them beneficial?
The two additional coordinate systems are cylindrical and spherical coordinate systems. A reason for converting from a Cartesian to cylindrical or spherical coordinate system may be to make an integral simpler to integrate and to visualize it better geometrically.