2.2: The electric potential V in the space between two flat parallel plates 1 and 2 is given (in volts) by V = 1300 x², where x (in meters) is perpendicular distance from plate 1. What is the magnitude of the electric field at x = 1.5cm and what is its direction (away or towards plate 1)?

In old TVs, an electron gun accelerates electrons between two parallel plates 1.2cm apart using a 25kV potential difference. a. What is the electric field magnitude between the plates? b. If the electrons start at the negative plate at rest, with what speed will they hot the negative plate? (Note: this speed will be a significant fraction of the speed of light) 3.

1. Consider the Yukawa potential V = g²e T/TO T where r = √√x² + y² + z² and is the distance from the origin and ro is a constant. (This potential arises naturally in nuclear physics but we can imagine it being produced by a specific configuration of electric charge) i) Work in a suitable coordinate system and derive the electric field associated with this potential. ii) Compute the flux through a spherical Gaussian surface centred on the origin as a function of r. iii) Use the above result in the limit that r → ∞ to show that the total charge involved is zero.

The classic Millikan oil drop experiment was the first to obtain an accurate measurement of the charge on an electron. In it, oil drops were suspended against the gravitational force by a vertical electric field.  1a. Given the oil drop to be 0.99 μm in radius and have a density of 910 kg/m3: Find the weight of the drop. 1b.If the drop has a single excess electron, find the electric field strength needed to balance its weight.   This is not and will not be graded