Studying the potential [42]: # Do not modify this function import numpy as np # Create a function giving the potential of the atom. # It is defined for x positive only located between 0 and the infinite. The potential barreer is centered at x = 0.5 def potential(x): if (x >= 0.8): return 0 return 0.5*np.e**-(((x-0.5)/0.1)**2) + np.e** (10*(1-x)) / 10000 + np.log(x+0.2) Your professor has created a function giving the potential of an atom as a function of the distance to the center of the atom. The units are arbitrary, as the values of the potential Task 1 Plot the potential and explain with your own words what this potential represents. You will need for this to use the explanations of the lectures, and it is also possible to have some help from the internet. Task 2 Explain how you will solve the following problem: you want to study the wave function evolution of a particle initially trapped into this potential, as a function of the energy of that particle. You will need to define the following: ⚫ which regions of interest you will use to split the problem ⚫ what are the conditions on the energy for each of these regions ⚫ what are the boundaries conditions at the limits of the regions Task 3 Solve mathematically the problem to reach the equations of the coefficients of the wave function. Your professor will not need to have the mathematical solution, but you will need to write down below the equations you obtained

3. Determine the motion, qualitatively, of a positive particle given the following lines of constant electric potential. Briefly explain why your reasoning regarding the motion of the particle. + of originally LOULET -V-IV IV/7V -3 OV 3V -15V 15V

2. Given the potential field V = 50(x2 - y2)V at point P (-4, 1, 5) that is stipulated to lie on a conductor-free space boundary. Find potential V, electric field Ē,electric field intensity D and ps at point P. Write the equation of the conductor surface.

SupercapacitorA typical symmetrical supercapacitor having carbon-based electrodes (activated carbon) in an aqueous electrolyte is shown here. Answer the following questions. 1. How does an electric double layer in a supercapacitor ensure higher capacitance than an electrostatic capacitor? 2. If activated carbon is coated with a thin layer of RuO2, will there be any effect on the performance of this supercapacitor? Why? 3. Potential has a significant role in increasing the energy density of the device (E= 1/2 CV2). How can working potential of this capacitor be increased? List any two approaches. 4. If the capacitance of one electrode is 200F, calculate the capacitance of the entire supercapacitor.

A thin spherical shell with radius R1 = 4.00 cm is concentric with a larger thin spherical shell with radius R2 = 6.00 cm. Both shells are made of insulating material. The smaller shell has charge q1 = +6.00 nC distributed uniformly over its surface, and the larger shell has charge q2 = - 9.00 nC distributed uniformly over its surface. Take the electric potential to be zero at an infinite distance from both shells. - For related problemsolving tips and strategies, you may want to view a Video Tutor Solution of Potential vsurface and field magnitude esurface at the surface. ▶ Part A Part B