A point charge +q is at the origin. A spherical Gaussian surface centered at the origin encloses +q. So does a cubical surface centered at the origin and with edges parallel to the axes. Select "True" or "False" for each statement below.

1. Suppose (for this statement only), that q is moved from the origin but is still within both the surfaces. The flux through both surfaces is changed.

2.If the radius of the spherical Gaussian Surface is varied, the flux through it also varies.

3. The area vector and the E-Field vector point in the same direction for all points on the spherical surface.

4. The E-Field at all points on the spherical surface is equal due to spherical symmetry.

5. The Electric Flux through the spherical surface is less than that through the cubical surface.

I tried :( F , T, F, T, F) but it is wrong, and I don't know which one is wrong.

A parallel-plate capacitor with circular plates and a capacitance of 10.3 μF is connected to a battery which provides a voltage of 11.2 V .

What is the charge on each plate?

How much charge would be on the plates if their separation were doubled while the capacitor remained connected to the battery?

How much charge would be on the plates if the capacitor were connected to the battery after the radius of each plate was doubled without changing their separation?

A particle moves along the x axis. It is initially at the position 0.200 m, moving with velocity 0.140 m/s and acceleration -0.410 m/s2. Suppose it moves with constant acceleration for 5.50 s.

We take the same particle and give it the same initial conditions as before. Instead of having a constant acceleration, it oscillates in simple harmonic motion for 5.50 s around the equilibrium position x = 0. Hint: the following problems are very sensitive to rounding, and you should keep all digits in your calculator.

a) Find the angular frequency of the oscillation. Hint: in SHM, a is proportional to x.

b) Find the amplitude of the oscillation. Hint: use conservation of energy.

c) Find its phase constant ϕ0 if cosine is used for the equation of motion. Hint: when taking the inverse of a trig function, there are always two angles but your calculator will tell you only one and you must decide which of the two angles you need.

d) Find its position after it oscillates for 5.50 s.

e) Find its velocity at the end of this 5.50 s time interval.

In this chapter we are looking at the differential equations that govern RC circuits. For a capacitor that is discharging, we know that going around the circuit the voltage should sum to zero:

Vc + Vr = 0.

Written in terms of charge and current, this is:

q/C = - i R.

Rewritten, q/C = -dq/dt R.

What this is telling us is that the current is being set by the charge on the capacitor. We can use a numerical approach to model this system. We know that dq/dt is a change in charge divided by a change in time:

Δq/Δt or (qf-qi)/Δt, where qi is the initial charge and qf is the final charge.

Treating q as qi, this allows us to state:

qi/C = -(qf-qi)/Δt.

Solving for qf, we get:

qf = qi – (qi/RC) Δt.

qf = qi (1 – Δt/RC).

In other words, at each small step in time, we subtract off a value proportional to the current charge.

We can model this behavior in a spreadsheet. We’ll use some tricks to help us out. In the top of the spreadsheet we’ll define four quantities: Δt, R, C and qi. This gives us details of the circuit and also the change in time. I put in some sample values, feel free to change them in order to experiment with how circuits work.

We then set up three columns. The first is a time column, the second is qi and the third is qf. Let’s look at first row. Time initial is zero, charge initial is set by the variables at the top of the chart and qf is done by formula, it is qi multiplied by (1–Δt/RC). Note that these values use absolute relationships, eg. $B$2, so if the formula gets copied, then it always refers back to the values at the top of the chart.

The next line down is really the key to the whole affair. The time column is the time from the line above, plus the delta t. The qi is the qf from the previous line, and the qf is calculated from the qi on this line. Note that since so many of the entries are in reference to the previous line, we can simply copy this expression to the line below to now have a three-step process. In fact, we can do this repeatedly (I did it 500 times) to watch how q changes from step-to-step in time. I graphed the q(t) behavior, and you can see it is an exponential, just as predicted by theory.

For this week’s homework, add a battery to this circuit and make a new spreadsheet that corresponds to charging up an empty capacitor. Your spreadsheet should include the appropriate graph. Note that for things like RC circuits, it is usually simpler to just solve the differential equation. For more complex problems, scientists and engineers will often use numerical methods rather than directly tackle hard math problems.

1. Polarizing sunglasses: (i) What direction are they polarized? (sketch), (ii) Why is 50% of sunlight removed? (iii) Why is horizontal glare screened out but not vertical glare? (second sketch)

light from a discharge tube containing a particular gas illuminates a diffraction grating and is observed on a screen 75.0cm behind the grating. The emission at wavelength 621nm creates a first-order bright fringe 38.0 cm from the central maximum. What is the wavelength of the bright fringe that is 47.3cm from the central maximum?

Projectile Motion - (Time) Above Ground - General Launch Angle

At a height h = unknown above the ground a rocket is fired at an initial speed v0 = 142.0 m/s at an angle θ = 42° above the horizontal. After a time = 25.2 s the rocket hits the ground. Ignore air resistance.

The magnitude of the gravitational acceleration is 9.8 m/s2.

Choose the RIGHT as positive x-direction. Choose UPWARD as psotitive y-direction

Keep 2 decimal places in all answers

Find v0x, the x component of the initial velocity (in m/s)

Find v0y, the y component of the initial velocity (in m/s)

(a) What maximum height (in meters) above the intial location does the rocket reach?

(b) How long (in seconds) does it take the rocket to reach the maximum heght?

(c) What is the range R (the horizontal distance) (in meters) traveled by the rocket before hitting the ground?

What is the rocket's initial height h (in meters) above the ground? Report h as positive.

(d) What is the vertical component of the velocity (in m/s) just before the rocket hits the ground? Pay attention to the direction (the sign).

(e) What is the magnitude of the velocity (including both the horizontal and vertical components) (in m/s) of the rocket just before it hits the ground?

(f) What is the direction of the velocity of the rocket just before it hits the ground?

Report the direction by an angle COUNTERCLOCKWISE from the +x axis.

a) Consider the excited state of beryllium with an electron configuration of 1s22s2p.      (i) What is the degeneracy of this electron configuration (i.e., how many distinct sets of quantum numbers are consistent with this configuration)?    [Note: The 2s and 2p electrons are in different sub-shells.]

   (ii) Determine the set of "term symbols" (e.g., 1S0, 3P2, etc.) for this configuration and the degeneracy of each of them. Confirm that the sum of the degeneracies is equal to your answer in (i).

b) Consider the electron configuration of titanium (1s22s22p63s23p64s23d2).

(i) Show that the possible states for this electron configuration are 1S, 1D, 1G, 3P, and 3F.   [Hint: For two electrons in the same sub-shell, the spatial state is symmetric for even L and antisymmetric for odd L.]

(ii) Determine the values of J associated with each of these term symbols and show how Hund’s rules determine which of these states has the lowest energy.

Projectile Motion - Rocket Clears Wall - General Launch Angle

A rocket is fired at an initial speed v0 = 165.0 m/s from ground level, at an angle θ = 50° above the horizontal.

A wall is located at d = 67.0 m. Its heigh is h = 47.0 m. Ignore air resistance.

The magnitude of the gravitational acceleration is 9.8 m/s2.

Choose the RIGHT as positive x-direction. Choose UPWARD as psotitive y-direction

Find v0x, the x component of the initial velocity (in m/s) . Keep 2 decimal places.

Find v0y, the y component of the initial velocity (in m/s) . Keep 2 decimal places.

You will calculate the time at which the rocket flies over the wall.

To find this time, should you use the horizontal (x) motion or the vertial (y) motion?

(a) At what time (in seconds) (after being fired) does the rocket fly over the wall? Keep 4 decimal places.

Note: when the rocket flies over the wall, in general, the height of the rocket is not equal to the maximum height.

(b) What is the rocket's height (in meters) when it flies over the wall? Keep 3 decimal places.

(c) By how much (in meters) does the rocket clear the top of the wall? Keep 3 decimal places.

(d) What is the rocket's maximum height (in meters) above the ground? Keep 2 decimal places.

Suppose that we have two masses, m1 and m2, traveling at initial velocities v1i and v2i . After they collide, they will have velocities v1f and v2f . The collision will happen along a straight line, and there are no external forces involved.

Exercise 1 Let m1 = 0.20 kg, m2 = 0.50 kg, v1i = 0.50 m/s, and v2i = 0.0 m/s. If v2f = 0.286 m/s, what is v1f ?

For the collision above what are the initial and final kinetic energies? Is kinetic energy conserved in the collision?

Let m1 = 500 g, m2 = 500 g, v1i = 0.45 m/s, and v2i = 0.0 m/s. If v1f = 0.225 m/s, what is v2f ? Simply stated, what would you say about the two masses after the collision? What type of collision is this?

Find the total Coulomb force on the charge q , given that q=+1.00μC , qa=+2.00μC , qb=−2.00μC , qc=−3.00μC , q=+4.00μC . The square is 50.0 cm on a side.

6. Which type of instrument would best be used to look at a grain of wheat pollen.

a) optical microscope

b) radio telescope

c) transmission electron microscope

d) scanning electron microscope

e) variable electron microscope

14) Rutherford’s alpha particle -scattering experiment showed that most alpha particles directed toward a thin metallic foil passed through with only slight deviations. From this evidence we can conclude that.....

18. Two stars star A and star B are the same size. The temperature of star A is 8000 K and the temperature of star B is 4000 K. How do their total luminosities compare.

A major leaguer hits a baseball so that it leaves the bat at a speed of 31.9 m/s and at an angle of 35.6 ∘ above the horizontal. You can ignore air resistance.At what two times is the baseball at a height of 10.2 m above the point at which it left the bat? Give your answers in ascending order separated with comma. t1,t2 = s Previous AnswersRequest Answer Incorrect; Try Again; 2 attempts remaining Part BPart complete Calculate the horizontal component of the baseball's velocity at an earlier time calculated in part (a). vx = 25.9 m/s Previous Answers Correct Part C Calculate the vertical component of the baseball's velocity at an earlier time calculated in part (a). vy = m/s Previous AnswersRequest Answer Incorrect; Try Again; 2 attempts remaining Part D Calculate the horizontal component of the baseball's velocity at a later time calculated in part (a). vx = nothing m/s Request Answer Part E Calculate the vertical component of the baseball's velocity at a later time calculated in part (a). vy = nothing m/s Request Answer Part F

What is the magnitude of the baseball's velocity when it returns to the level at which it left the bat?

SubmitRequest Answer

Part G

What is the direction of the baseball's velocity when it returns to the level at which it left the bat?

magnitude of the baseball's velocity when it returns to the level at which it left the bat? v = nothing m/s Request Answer Part G What is the direction of the baseball's velocity when it returns to the level at which it left the bat? θ = nothing ∘ below the horizontal Request Answer Provide Feedback

hiker starts at his camp and moves the following distances while exploring his surroundings: 75.0 m north, 2.50 x 10^2 m east, 125 m at an angle 30.0

how do you find velocity and distace travelled from an acceleration time. graph? (given: Vo=0, car is moving in straight direction) graph is a piecewise { y=-x [0,5] and y=0 [5,infinity] }