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PHY2323 – Electricity and Magnetism Assignment 1
发布时间:2022-02-23
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PHY2323 – Electricity and Magnetism
Assignment 1
1. Imagine some space with a volumetric charge density of
(
) =
, centered at the origin. Determine an expression for the electrostatic field at a distance b away from the origin. It helps to note the spherical symmetry in this situation (i.e. use spherical coordinates!).
2. Consider a semi-spherical surface defined by =
;
<
<
/
;
<
<
. Determine the electric flux passing through this surface for an electric field
=
+
(
/
). [note that this E field is described using a mixture of Cartesian and Spherical variables!]
3. A semi-circular ring centered at the origin is located in the first quadrant (0 < ϕ < /
) of the x-y plane and carries a unform surface charge density of
=
, but only for a radius of a < ρ < b. The charge density is zero elsewhere. (k is a constant, and (ρ, ϕ, z) are the usual cylindrical coordinates.) Determine an expression for the the z-component of the electric field at any location on the z-axis. [NOTE: We are only asking for the z- component of the electric field. The x- and y-components exist but they are a little messy. You can certainly attempt to figure them out, but you don’t have to.]
4. Imagine half-circle of radius R in the XY plane that carries a 1-dimentional line of positive charge. This half-circle spans 0 ≤ ≤ 1800 . The total charge on the half-circle is Q. However, the linear charge density is NOT UNIFORM and is defined as
=
. What is the force felt by a particle of charge q0 located at the origin?