The gradient of a scalar field v is a vector that represents both the magnitude and direction of the maximum space rate of increase of v. obtain a mathematical expression for the gradient of v using calculus by evaluating the difference in field dv between two points on contours where v is a constant. show that the maximum rate of increase of v with respect to occurs when dil is the normal derivative dn.

High schoolphysics 5+3 pts a neon light consists of a glass tube with metal wires at each end. when connected to a high-voltage source, the gas glows. if a fly lands on the glass tube, what will most likely happen? a) the fly will not feel a shock because the glass conducts any free electrons back into the gas. b) electrons will flow directly from the metal wires along the glass and shock the fly. c) the fly will not feel a shock because the glass insulates it from the electrons in the gas and the metal. d) electrons that are moving through the gas will be conducted through the glass and shock the fly.