(3) The purpose of this problem is to find the electric field of a ring of charge located in the x – z plane and has a diameter d. The ring has a total charge Q. To accomplish this, we will break the ring of charge into point charges. All answers should be given in terms given parameters and the coordinate 0. The field point, P, is located at (0, yo, 0). (a) What is the charge dq of the point charges? (b) What is the value of î for the point charges: (c) What are the bounds of integration to find the total electric field? (d) If instead of a full ring, we have half of a ring, which (if any) of your answers to parts (a) - (c) change? Which (if any) will stay the same?

Suppose you design an apparatus in which a uniformly charged disk of radius R is to produce an electric field. The field magnitude is most important along the central perpendicular axis of the disk, at a point Pat distance 2.90R from the disk (see Figure (a)). Cost analysis suggests that you switch to a ring of the same outer radius R but with inner radius R/2.90 (see Figure (b)). Assume that the ring will have the same surface charge density as the original disk. If you switch to the ring, by what part will you decrease the electric field magnitude at P? (a) (b) Number i Units

A disk with radius R and uniform positive charge density o lies horizontally on a tabletop. A small plastic sphere with mass M and positive charge hovers motionless above the center of the disk, suspended by the Coulomb repulsion due to the charged disk. At what height h does the sphere hover? Express your answer in terms of the dimensionless constant v = 20 Mg/ (Qo). Express your answer in terms of some or all of the variables R and v. h = R- 1-v √(2-v)v Submit Part C h = Previous Answers Correct If M = 300 g, Q = 1.0 μC, R = 6.0 cm, and o = 10 nC/cm², what is h? Express your answer with the appropriate units. μᾶ Value 2 Units Submit Previous Answers Request Answer ? <

Early in the 20th century, a leading model of the structure of the atom was that of English physicist J. J. Thomson (the discoverer of the electron). In Thomson’s model, an atom consisted of a sphere of positively charged material in which were embedded negatively charged electrons, like chocolate chips in a ball of cookie dough. Consider such an atom consisting of one electron with mass m and charge -e, which may be regarded as a point charge, and a uniformly charged sphere of charge +e and radius R.  By that time time, it was known that excited atoms emit light waves of only certain frequencies. In his model, the frequency of emitted light is the same as the oscillation frequency of the electron (s) problems in the atom. What radius (in millimeter) would a Thomson-model atom need for it to produce red light of frequency 4.57 x 1014 Hz? (Don't express your answer in scientific notation)