# Problem 1 The atomic nuclei in a metal crystal resting on the surf...

## Question

Problem 1
The atomic nuclei in a metal crystal resting on the surface of the Earth would fall to the bottom of the metal if gravity were the only force acting on them. The gravitational force must be balanced by a small electric field. For a metal of atomic number Z and atomic mass A find an expression for the magnitude and direction of this electric field. Give a numerical value for copper, Z = 29, A = 63. You may find it useful to know that on the surface of the Earth, the acceleration of gravity is g = 9.807 m/s², and that the masses of the proton and neutron are mp = 1.672×10⁻²⁷ kg and mn = 1.674×10⁻²⁷ kg. The fundamental unit of charge is e = 1.602×10⁻¹⁹ C.

Problem 2
A long length of cylindrical conducting wire of diameter 2.05 mm is charged so that is carries λ coulombs per meter. What is the maximum linear charge density λ the wire can carry and still avoid electrical break down of the surrounding air? Air will suffer breakdown if the electric field exceeds a magnitude of 3 × 10⁶ N/C.

Problem 3
Two large, flat plates are arranged vertically so that they are parallel to each other separated by 10.0 mm. Each carries charge density σ = +42 nC/m². The plate on the right has a small, circular hole cut into it of radius r = 5.0 mm. An electron is placed at the center of the hole. Calculate the acceleration of this electron when it is at the center of the hole and when it reaches a point midway between the two plates. (Hint, use superposition. If required, the mass of the electron is me = 9.11 × 10⁻³¹ kg).

Problem 4
Two metal spheres of radii R₁ = 1 cm and R2 = 3 cm are well separated from each other but are connected by a thin conducting wire. A total charge Q = +100 nC is placed on the conductors. How much of it will be held by Sphere 1 and how much by Sphere 2? What is the voltage of each sphere?
The spheres are separated enough from each other that you may neglect any interactions between them so that it may be assumed that any charge distributes itself uniformly on each sphere. The wire is thin enough that it does not alter the otherwise perfectly spherical shape of the conductors.
Hint: Find the electrical potential of each sphere if they carry charges q₁ and q₂ where q₁ + q₂ = Q. Then use what you know about the voltages to solve for q₁ and q₂.

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