PHY2323 – Electricity and Magnetism Assignment 2
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PHY2323 – Electricity and Magnetism
Assignment 2
1. A hemispherical shell (half-sphere → like a bowl) of radius a = 30 cm, centered at the origin (i.e. the same center that the complete sphere would have), carries a surface charge density of = (). This half-sphere covers ≤ ≤ and ≤ ≤ . [the charges on this surface are negative]
a. Determine the electrostatic potential at the centre of this hemisphere (in volts).
b. What velocity does an electron ( = − . × − ; = . × − ) achieve if you release it from rest at the origin? [The electron will experience a repulsive electrostatic force and accelerate away towards infinity. We are asked to determine its velocity when it reaches infinity. Assume that the only force acting on the electron is this electrostatic force. [Hint: kinetic energy = ]].
2. Imagine a conducting metal sphere of radius a = 2 cm that carries a total charge Qa = 8 nC (8x10-9 C) that is uniformly distributed on its surface. A concentric spherical shell of radius b = 3 cm carries a total charge Qb = -8 nC. Both the central sphere and the other shell are centered at the origin.
a. What is the electrostatic potential difference of a point located at (0,0,2) cm with respect to the potential at the point (3,3,0) cm? [please note that these points are expressed in rectangular coordinates, while you should probably work in spherical when doing your calculations]
b. What is the electrostatic potential difference of a point located at (0,0,2) cm with respect to the potential at the point (8,0,0) cm? [please note that these points are expressed in rectangular coordinates, while you should probably work in spherical when doing your calculations]
3. A very long conducting rod (cylindrical in shape) is held in water. The radius of the rod is 20 mm. An external electrostatic field exists in the water and is = + (volts/metre). If the rod is aligned with the z axis, come up with an expression for the surface charge density on the surface of the rod. [ = and = ]
2022-02-23