how should the integral in gauss's law be evaluated?

A uniform electric field exists in the region between two oppositely charged plane parallel plates. A proton is released from rest at the surface of the positively charged plate and strikes the surface of the opposite plate, 1.60 cm distant from the first, in a time interval of $3.20 \times 10^{-6} s$. (a) Find the magnitude of the electric field. (b) Find the speed of the proton when it strikes the negatively charged plate.

A mixture of methanol and methyl acetate contains 15.0 wt% methanol. (a) Using a single dimensional equation, determine the g-moles of methanol in 200.0 kg of the mixture. (b) The flow rate of methyl acetate in the mixture is to be 100.0 lb-mole/h. What must the mixture flow rate be in $\mathrm{lb}_{\mathrm{m}} / \mathrm{h}$ ?

If r=⟨x, y⟩, r1=⟨x1, y1⟩, and r2 = ⟨x2, y2⟩, describe the set of all points (x, y) such that |r - r1| + |r - r2| = k, where k > |r1 - r2|.

Draw the structural formula and place a partial positive and a partial negative charge on each atom in $\mathrm{HCl}$ molecule.

Is the molecule polar? Explain your reasoning.

How many carbon-carbon sigma bonds are present in each of the following molecules:
cyclobutane.

Which of the following describes the bonding in HNNH?

A) sp orbitals on each nitrogen overlap and form a sigma bond

B) sp orbitals on each nitrogen overlap and form a pi bond

C) sp2 orbitals on each nitrogen overlap and form a sigma bond

D) sp2 orbitals on each nitrogen overlap and form a pi bond

E) p orbitals on each nitrogen overlap and form a sigma bond

What is the electron configuration of $\ce{Mg+}$ ?

Imagine two 1.0-g bags of protons, one at the earth’s north pole and the other at the south pole. (a) How many protons are in each bag? (b) Calculate the gravitational attraction and the electric repulsion that each bag exerts on the other. (c) Are the forces in part (b) large enough for you to feel if you were holding one of the bags?

Imagine two 5.0 g bags of protons, one at the earth's north pole and the other at the south pole.

What is the best explanation for the observation that the electric charge on the stem became positive as the charged bee approached(before it landed)?
A. Because air is a good conductor, the positive charge on the bee'ssurface flowed through the air from bee to plant.
B. Because the earth is a reservoir of large amounts of charge, positive ions were drawn up the stem from the ground toward the charged bee.
C. The plant became electrically polarized as the charge was approached.
D. Bees that visited the plant earlier deposited a positive charge on the stem.

A 5.00 g charged insulating ball hangs on a 30.0 cm long string in a uniform horizontal electric field as shown in Figure mentioned. Given the charge on the ball is $1.00 \mu \mathrm{C}$, find the strength of the field.

Point charge q1 = -5.00 nC at the origin and point charge q2 = +3.00 nC is on the x-axis at x = 3.00 cm. Point P is on the y-axis at y = 4.00 cm.

a. Calculate the electric fields E1 and E2 at point P due to the charges q1 and q2. Express your results in terms of unit vectors.

b. Use the results of part (a) to obtain the resultant field at P, expressed in unit vector form.

Point charge $q_{1}=-5.00 \mathrm{nC}$ is on the x-axis at x=-0.400 m. Point P is on the x-axis at x=+0.200 m. Point charge $q_{2}$ is at the origin. What are the sign and magnitude of $q_{2}$ if the resultant electric field at point P is zero?