Question Solved1 Answer The figure (Figure 1) shows a thin rod of length L with total charge Q. Part A Find an expression for the electric field strength on the axis of the rod at distance r from the center. Express your answer in terms of the variables L, Q, T, and appropriate constants. EVO AXO ? E = Submit Request Answer Figure < 1 of 1 > Part B Verify that your expression has the expected behavior if r >>L. Express your answer in terms of variables Q,r and constants , E0. L IVO ALO ? + + + + + + + + + + + + E = Submit Request Answer - Part C Evaluate E at r = 4.9 cm if L = 5.0 cm and Q = 3.6 nC. Express your answer to two significant figures and include the appropriate units. HÅ ? E = Value Units Submit Request Answer

2. A ring of radius R has a non-uniform linear charge density ſto cos(0) O<O<A, (0) = Lo sin(0) <O< 27, where 0 is measured as shown in the figure and do is a positive constant. (a) What is the net charge of this ring? (b) Find the electric field at the center of the ring.

6. Let S be the set of perfect binary trees, defined as: • Basic step: a single vertex v with no edges is a perfect binary tree T.. Recursive step: if T is a perfect binary tree, then a new perfect binary tree T' can be constructed by taking two copies of T, adding a new vertex v, and adding edges between v and the roots of each copy of T Prove that h(T) = log2(n(T) + 1) – 1 for any perfect binary tree T, where n(T) is the number of vertices of T and h(T) is the height of T.

Question 3 1 pts Molecules that contain a large number of functional groups that can interact with other functional groups on other molecules tend to have high boiling points because these interactions have to be broken for the molecules to separate from one another O tend to have low boiling points because the interactions make it hard to separate molecules from one another tend to have high boiling points because these interactions must be broken, AND bonds within the molecule must be broken in order to boiling to occur O tend to boil very easily because these interactions are easier to break than bonds withing a molecule

1. A 24.47 gram sample of copper is heated in the presence of excess chlorine. A metal chloride is formed with mass of 38.12 gram. Determine the empirical formula of the metal chloride. 2. A 61.73 gram sample of copper is heated in the presence of excess oxygen. A metal oxide is formed with a mass of 69.50 g. Determine tge empirical formula of the metal oxide.3. A 6.250 gram sample of iron is heated in the presence of excess bromine. A metal bromide is formed with a mass of 33.07 g. Determine the empirical formula of the metal bromide.

An electric dipole with dipole moment p⃗ p→ is in a uniform external electric field E⃗ E→. Part A Part complete Find the orientations of the dipole for which the torque on the dipole is zero measured counterclockwise from the electric field direction. Enter your answers in degrees separated by a comma. θθ = 0,180 ∘∘ SubmitPrevious Answers Correct Part B Part complete Which of the orientations in part A is stable, and which is unstable? (Hint: Consider a small rotation away from the equilibrium position and see what happens.) The orientation is stable only when p⃗ p→ and E⃗ E→ point in the same direction. The orientation is stable only when p⃗ p→ and E⃗ E→ point in opposite directions. Both orientations in part A are stable. Both orientations in part A are unstable. SubmitPrevious Answers Correct Part C Choose a figure that correctly shows the dipole's own electric field and the external electric field for the stable orientation in part B. Choose a figure that correctly shows the dipole's own electric field and the external electric field for the stable orientation in part B.

Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. y = tan(x) 3t + t dt 3 Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. tan(x) y = ' 3t+ V7 dt r = sec?(x)V3 tan(x)V tan(x)