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How can we show that the individual field lines obey Gauss' law? How would this be different from showing that Gauss' law is satisfied for the field?

As stated in the problem, I want to demonstrate mathematically that field line density is directly related to the magnitude of B. How would I be able to do this, other than simply using the flux equation and showing that for a higher flux in the same area, the magnetic field must be rise...

Could you explain how the result is approximate? The instructor wanted us to use the error propagation formula specified to find the uncertainty in the standard deviation, so I believe they expected us to use this method. Would it be possible to get rid of the second summation term under the...

Using this error propagation formula: I expressed the standard deviation (s) and the partial derivatives of s w.r.t. each data point as: This gives me an uncertainty of: , where m is the mean. Does this seem reasonable for the uncertainty of the standard deviation? I also found the thread...

I was able to figure out this problem.

The original differential equation is: My solution is below, where C and D are constants. I have verified that it satisfies the original DE. When I apply the first boundary condition, I obtain that , but I'm unsure where to go from there to apply the second boundary condition. I know that I...

Thank you so much for the help, I was able to get it to work!

Redefined cell 11 as being +4 and being material 3 (coolant), but still getting the same error. Yes, the last line in the fill should have been 3 3 3 3 3.

The Geometry.txt file extension should be changed to .i to run it in MCNP.

MCNP6 gives me a "10 particles got lost" error when I try to run the attached input file modeling a 3x3 fuel lattice surrounded in coolant. As I understand it, this error is usually related to the geometry/surface definitions of each component, but I'm unsure of what the source of the error is...

According to the page below, the average energy of a particle in the nth state is given by n^2*pi^2*h_bar^2 / 2m. https://cnx.org/contents/pZH6GMP0@1.185:Ek7FZdR3@3/The-Quantum-Particle-in-a-Box I initially tried finding <E> using the Hamiltonian operator, but the integral required to...

I first normalized the given wavefunction and found the value of n that satisfies the normalization condition. I then used E = <E> = pi^2* h_bar^2* n^2/(2*m) to get the expectation value of energy. Assuming that this was the right process, I'm now trying to find <E^2> using the same equation...

I am trying to find the mass flow rate of coolant through a channel within a hexagonal nuclear fuel assembly. I am given the specific heat of the fluid, the coolant inlet and outlet temperatures, the total power produced by a single fuel pin, the diameter of the fuel pin, the length of the fuel...

Let's say we have a cylindrical fuel pin with fissile material in the middle, followed by a gas gap and cladding material. It is being cooled by water on the outside. The temperature drop through the fissile material should be parabolic due to heat generation, and the temperature drops through...

I want to use the point reactor kinetics equations to solve for the power as a function time when a reactivity of gamma*t is added to a reactor that is at equilibrium at time 0. I am also asked to consider the case where the transients are long-lived compared to the lifetime of prompt neutrons...

I feel like I am. I've been staring at the energy and momentum conservation equations to try to find something more "sophisticated," but that doesn't seem to work out since we don't have enough information (e.g. the scattering angle or velocities of the electron-positron pair).

In most textbooks, the recoil energy of the nucleus is ignored as it absorbs so little energy, and since its main role in the reaction is to absorb some of the photon's momentum without absorbing much energy. I'm tempted to say that the nucleus gets the maximum energy when the kinetic energy of...

I see, that makes sense. Thank you for the help!

Ok. Is there any way of demonstrating that the solutions are equivalent? How does having a complex number in the constant not affect the significance of the wavefunction?

Using the boundary conditions where psi is 0, I found that k = n*pi/a, since sin(x) is zero when k*a = 0. I set up my normalization integral as follows: A^2 * integral from 0 to a of (((exp(ikx) - exp(-ikx))*(exp(-ikx) - exp(ikx)) dx) = 1 After simplifying, and accounting for the fact that...

Shear force is positive at the left support, negative at the right support, and zero at the center of the beam. I don't fully understand how to connect the shear force along the length of the beam to its stress. I see how the shear stress varies vertically, but not horizontally along the axis of...

I know that shear stress in horizontal beams has a parabolic distribution, so that the max shear stress occurs at the neutral axis. I also understand that for a beam subject to a distributed load with supports at its ends, the magnitude of the shear force is highest at the left and right ends of...

I am reading about beams under distributed loading and shear stresses and needed to use the equation τ = VQ/It, where Q is the first moment of area. I understand that Q is zero about the neutral axis, and that this is, in fact, how the neutral axis is defined. The first moment of area above the...

Oops...I used the same time of flight as for the previous problem. The new time is 100 = 50cos25 * t ---> t = 2.2 s So, 40 - y0 = y0 + 50sin25*2.2 - 1/2(9.8)(2.2)^2 --> y0 = 8.6 m

With v0 = 50 m/s, I get y0 = 973 m, which still doesn't meet the criterion that y0 < yf. I have a very similar problem with v0 = 8 m/s, θ = 35 degs, x = 7 m, yf = 3 m, and mass of object = 2 kg. I'm having the same problem with that too.

What would be the approach to solving the problem if the target were not as far away?

First, I tried solving for the total time of flight, which I got as 100 = 5cos25*t --> t=22 s Since we know the height at which the object lands, but not at which it is launched, I tried setting up the equation as: yf = 40 - y0 = y0 + 5sin25*(22) - 1/2(9.8)(22)^2 However, I got y0 = 1183 m...

Thanks for the explanation. This makes a lot of sense. Somehow, I assumed that the signs were supposed to "carry over" to the stresses in compression and tension, and I didn't think of them as having separate meanings.

I have recently learned that, by convention, axial tensile stresses are positive and axial compressive stresses are negative. I am having some trouble incorporating this information into my FBDs that are used to find the axial forces leading to these stresses. For instance, from the attached...

Homework Statement I'm a bit confused on when a force creates a moment about a point, and when it does not. In particular, in the attached diagram, would F be able to produce a moment about point A? I initially thought that wouldn't be possible as A lies on the same line as F, but since F does...

I'm doing problems on finding row and column spaces. My textbook tells me to find the echelon form of the matrix, and then to identify the bases. My question is, can I reduce the matrix to reduced echelon form to get the bases? I have the same question about bases for the solution space.

Homework Statement I have a question about the pulley problem in the attachment. Homework Equations This question can be answered using equilibrium of forces, namely Fx = 0 and Fy = 0. The Attempt at a Solution The answer key states that for the sum of the x-components, we should use the...

The voltage drop across R4 is 12 - 6.17 - 1.71 = 4.12 V.

I finally solved it. I think the most helpful thing is to notice that the equivalent resistance in a parallel circuit is less than each of the individual resistors. Thanks for all the help!

Homework Statement I'm asked to find a combination of resistors (parallel and/or series) that uses resistors of 25 Ω, 100 Ω, 50 Ω, and 50 Ω. They should add up to give a total resistance of 62.5 Ω. Homework Equations Req for parallel = 1/R1 + 1/R2 + ... Req for series = R1 + R2 + ... The...

Would we work backwards to get 12 - 6.17 - 1.17 = 4.66, and divide that by 3?

12/17.5 = 0.69 0.69 * 9 = 6.17 volts

Would the voltage going through R4 be different from 12 V?

For R2, the voltage is 0.69 * 2.5 = 1.725. I don't know how I ended up with 1.17. For R4, I thought it was in parallel and did 12 = 9 * I to get I = 1.33 amps.

Here are the calculations I have so far: R1: 0.69 amps, 6.17 volts R2: 0.69 amps, 1.17 volts R4: 1.33 amps, 12 volts For R3 and R5, am I supposed to consider them to be in series with the battery, or in parallel?

Homework Statement I'm asked to find the voltage, current, and resistance through each resistor in the given circuit. Homework Equations Req for parallel = 1/R1 + 1/R2 + ... Req for series = R1 + R2 + ... The Attempt at a Solution First, I want to find the total resistance in the circuit...

In 1/2kx^2, k refers to the spring constant and x to the amount of stretch in meters. In Fd, d refers to the distance I need to pull back the clothespin, and x functions the same way in the above equation. The rubber band should be placed horizontally (perhaps right next to a table with rods...

The formula for the elastic potential energy is 1/2kx^2. I'm trying to find the value of d that would allow the clothespin to touch the ceiling upon release, so I haven't chosen a value for that. The distance to the ceiling was chosen as the height because that is how far the pin would be from...

Homework Statement I'm trying to figure out the setup of an experiment I have to complete. The experiment calls for a rubber band to be secured by rods on the sides, and for a clothespin to be attached to the rubber band. I have to figure out how far back the clothespin needs to be pulled down...

That was a typo...I meant that since the 30 ohm and 40 ohm resistors are in series (not parallel), the current is the same at both places. Thank you for all the help!

The total resistance is 95 ohms and the total voltage is 12 volts. The total current is 12/95 amps, and since this is a parallel connection the current is the same at both resistors. Then the voltage of the 40 ohm resistor is 12/95 * 40 = 480/95 volts. The voltage of the 30 ohm resistor is 12/95...

Is it correct that the current is 3.16/50 amps for each of the 50 ohm resistors? Are the values for the voltage drop of the other two resistors correct?

If I use a 25 ohm resistor in place of the 50 ohm ones, is the circuit now considered to be in series completely? If that's the case, then the total resistance is 95 volts and the current across this 25 ohm resistor is 12/95 amps. V = IR V = 12/95 * 25 = 3.16 volts For the current, is it I =...

Homework Statement 1. Use resistors of 30 ohms, 40 ohms, 50 ohms, and 50 ohms to create a circuit with a total resistance of 95 ohms. 2. Find the amount of current going through two of these resistors if the circuit is attached to a source of 12 v. 3. What would be the voltage drops for the...

Imagine that one person is on one side of a hall, and another person is on the other side. There is a gap in the wall that separates the two people. In that case, how is it possible that one person can hear the other person, but cannot see them unless in a direct line with them?