Physics 2A03 Assignment #1 : Fe/E
1)Two 2.00-μC point charges are located on the x axis. One is at x = 1.00 m, and the other is at x = –1.00 m.
a) Determine the electric field on the y axis at y = 0.500 m.
b) Calculate the acceleration of an electron placed on the y axis at y = 0.500 m.
2)Two identical particles, each having charge +q, are fixed in space and separated by a distance d. A third point charge –Q is free to move and lies initially at rest on the perpendicular bisector of the two fixed charges a distance x from the midpoint between the two fixed charges.
a) Show that if x is small compared with d, the motion of –Q will be simple harmonic along the perpendicular bisector. Determine the period of that motion.
b) How fast will the charge –Q be moving when it is at the midpoint between the two fixed charges, if initially it is released at a distance a d from the midpoint?
3)A uniformly charged thin-walled right circular cylindrical shell has a total charge Q, radius R, and height h, and is aligned with the x-axis.
a) Determine the electric field at a point a distance d from the right side of the cylinder.
b) Consider now a solid cylinder with the same dimensions and carrying the same charge, uniformly distributed through its volume. Determine the electric field at a point a distance d from the right side of the cylinder.
(Suggestion: slice the cylinder intodisks of thickness dx, and use the expression for the field of a disk derived in class and/or in Serway).
4) A simple electric quadrupoleconsists of a charge +2q at the origin, and two charges, each of –q, at x = –a andx = +a on the x axis.
a) Find an expression for the electric field on the positive x axis.
b) Using the expression derived in a), show that the field is proportional to the inverse fourth power ofdistance, for distances x a.
(Hint: Write in terms of the dimensionless parameter u = a/x, andexpand in a Taylor series.)
Turn over…
5) The finite sheet 0≤x≤1, 0≤y≤1 on the z=0 plane has a charge density of ρ=xy(x2+y2+25)3/2 μC/m2.
a) Find the total charge on the sheet.
b) Make a plot the charge distribution.