Magnetic field penetration in a plate. The penetration equation may be written as , where lambda is the penetration depth, (a) Show that B(x) inside a superconducting plate perpendicular to the x axis and of thickness delta is given by where Bn is the field outside the plate and parallel to it; here x = 0 is at the center of the plate, (b) The effective magnetization M(x) in the plate is defined by B(x) = Ba = 4 pi M(X). Show that, in CCS. In SI we replace the 4 pi by mu 0.
Answers
In a superconducting plate perpendicular to the x-axis and of thickness δ, the magnetic field inside the plate, B(x), is given by B(x) = Bn * e^(-x/λ), where Bn is the field outside the plate and parallel to it. The penetration depth, λ, determines the rate of decay of the magnetic field inside the plate. In cgs units, the effective magnetization, M(x), is defined as M(x) = B(x)/(4π). In SI units, it is given by M(x) = B(x)/μ₀, where μ₀ is the permeability of free space.
(a) To show that B(x) inside a superconducting plate perpendicular to the x-axis and of thickness δ is given by B(x) = Bn * e^(-x/λ), where Bn is the field outside the plate and parallel to it, we can utilize the penetration equation.
The penetration equation states that the magnetic field inside a superconductor decays exponentially with distance from the surface, and the penetration depth (λ) determines the rate of decay.
Let's consider a coordinate system where x = 0 is at the center of the plate. The field inside the plate, B(x), will depend on the distance from the center (x) and can be expressed as B(x) = Bn * f(x), where f(x) is a function to be determined.
At the center of the plate (x = 0), the field should be equal to the field outside the plate, B(0) = Bn. Therefore, f(0) = 1.
Using the penetration equation, we know that the field decays exponentially as we move away from the surface. This can be represented as f(x) = e^(-x/λ), where λ is the penetration depth.
Hence, the expression for B(x) inside the superconducting plate is B(x) = Bn * e^(-x/λ).
(b) The effective magnetization M(x) in the plate is defined by B(x) = Ba = 4πM(x), where Ba represents the applied magnetic field and M(x) is the magnetization.
In the cgs (centimeter-gram-second) system, the relation is given by B(x) = Ba = 4πM(x).
However, in the SI (International System of Units) system, we replace 4π with μ₀, where μ₀ is the permeability of free space. Therefore, in SI units, the relation becomes B(x) = Ba = μ₀M(x).
This adjustment accounts for the difference in the definition of magnetic field and magnetization between the cgs and SI systems, where μ₀ is a constant that relates the two systems.
In summary, in the cgs system, the effective magnetization is related to the magnetic field by M(x) = B(x)/(4π), while in the SI system, it is given by M(x) = B(x)/μ₀.
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Related Questions
WILL GIVE BRAINLEIST
Which steps show how to use distributive property to evaluate 5 x 38
Answers
Answer:
The answer is most definitely A. It is the only answer that reaches the correct value of 190, which is what 5 * 38 equals. However, to put it into perspective...
Step-by-step explanation:
When we use the distributive property we are breaking down something sometimes, and in this case, very simple into a more extended form.
5 * 38 is the same as saying 5(40 - 2). We also know that if we subtract the sum of 5 * 2 from 5 * 40, it will end up the same as 5 * 38 because you are multiplying 5 two times less.
5 * 40 = 200
5 * 2 = 10
200 - 10 = 190
The answer is A
;)
which expression is equivalent to
Answers
You multiple the inside exponent and the out side exponent and is equal to 32
is 1.31 repeating (rational or irrational?)
Answers
Answer
rational
Step-by-step explanation:
it does repeat so it is irrational
Brainlist plz
The graph below shows the amount of money Alexia and Brent have in savings. a) Write an equation to represent the amount y that each person has in savings after x weeks: Alexia: Brent: b) Tell the story of the graph. Include what the point of intersection means in this problem. Savings (dollars) Brent Alexia 0 1 2 3 4 5 6 7 8 9 10 Time (weeks) S485241505 35 30
Answers
The equation representing the amount of money Alexia and Brent have in savings after x weeks is:
Alexia: y = -5x + 50
Brent: y = 10x + 30
The graph shows their savings over time, and the point of intersection represents the week when both Alexia and Brent have the same amount of money in savings.
In the given graph, the x-axis represents the time in weeks, while the y-axis represents the amount of money in savings. The data points on the graph indicate the savings for each person at different weeks. To represent this relationship mathematically, we can use linear equations.
For Alexia, we observe that her savings decrease by $5 every week, starting from $50. This can be represented by the equation y = -5x + 50, where y represents the savings and x represents the number of weeks.
On the other hand, Brent's savings increase by $10 every week, starting from $30. This can be represented by the equation y = 10x + 30.
The point of intersection on the graph represents the week when both Alexia and Brent have the same amount of money in savings. At this point, the y-values of both equations are equal, indicating that the savings of both individuals are equal. This intersection point represents the week when their savings are the same.
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Consider the following two probability distributions: Distribution A DistributionB x P(x) x P(x)0 0.20 0 0.011 0.20 1 0.022 0.20 2 0.943 0.20 3 0.024 0.20 4 0.01Which of the following is an accurate statement regarding these two distributions?Distribution A has a higher variance.Distribution B has a higher variance.Both distributions are positively skewed.Both distributions are uniform.
Answers
As per the probability, an accurate statement regarding these two distributions is option (a) Distribution A has a higher variance
Looking at the given probabilities for each value in Distribution A and Distribution B, we can calculate their respective means and variances. For Distribution A, the mean is 2.2 and the variance is approximately 1.76. For Distribution B, the mean is 1.02 and the variance is approximately 1.416.
Based on these calculations, we can see that Distribution A has a higher variance than Distribution B.
This means that the values in Distribution A are more spread out from the mean than the values in Distribution B.
Therefore, the accurate statement regarding these two distributions is that Distribution A has a higher variance than Distribution B.
Hence the option (a) is correct.
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PLZ HELP!!!!!! ASAP! 70 POINTS!
Factor ax^2−ay−bx^2+cy+by−cx^2
Answers
Answer:
(a-b-c)(X^2-Y)
Step-by-step explanation:
DONE!!
The table shows the distances between major cities.
New York to Paris 3,636 miles
Los Angeles to Toronto 2,171 miles
Mr. Santiago has a flight from Los Angeles to Toronto. If the plane travels at 520 miles per hour, how many hours long is the flight?
__ hours
Answers
Answer:
The time take for the journey can be calculated by dividing the total distance by the distance travelled in an hour.
Which is 2171 (Total distance) / 520 (Distance travelled in a hour)
\(2171/520 = 4.175\)
Which can be rounded of to 4.2
It takes 4.2 hours for the flight between Los Angeles and Toronto
Suppose you have two similar rectangular prisms. The volume of the smaller rectangular prism is 64 in³ and the volume of the larger rectangular prism is 1,331 in³. What is the scale factor of the smaller figure to the larger figure?
4:11
1:21
3:10
9:25
Answers
Answer: A 4:11
Step-by-step explanation:
The scale factor for volume is:
64:1331 > you are working with volume, you need to take
the cube root of the ratio because the dimensions are
cubed
∛64 : ∛1331
4:11
A
Use the information given to enter an equation in standard form.
Slope is -6, and (0,-7) is on the line.
Plzzz help I will mark you as brainliest
Answers
Answer:
y=-6x-7
Step-by-step explanation:
Explain what the graph of the function represents. Be sure to use complete sentences. f(x) = -2/3 + 490.
Answers
Answer:
parallel functions.
lines negative.
functions different in that they do not have the same y-intercept or x-intercept.
Step-by-step explanation:
from brainly
itisdougthepugs
1. y = -⅔x + 490
2. I would start with the y-intercept(490) on the graph. Then from that point, I would use rise/run to find the next point: I would go down two points (because the slope is negative), and run three points to the right.
3. f(x) = -⅔ + 490. The graph represents the total profits of last month.
4. View file below.
5. The graphs of these functions are similar in the fact that they are parallel to each other, therefore having the same slope.Both lines are also negative. They are different in that they do not have the same y-intercept or x-intercept.
Find the length of the hypotenuse. The measure of the hypotenuse?
Answers
Answer:
Since it's a right angled triangle
Hypotenuse = h
h² = 7²+24²
h= √49 + 576
h = √625
h= 25
Therefore hypotenuse is 25
Hope this helps.
Answer & Step-by-step explanation:
First, we must know the Pythagorean Theorem.
a² + b² = c²
a = 24
b = 7
Now, let's plug in these numbers into the formula.
24² + 7² = c²
Simplify the exponents.
576 + 49 = c²
Add 576 and 49 together.
625 = c²
Square root the terms on both sides of the equation.
√625 = √c²
Simplify the square roots.
25 = c
The length of the hypotenuse is 25 units.
it says to determine the scale factor and center of dilation that will carry ABCD onto A’B’C’D’ please help im stuck
Answers
Answer:
3/2
Step-by-step explanation:
\(A'B'=6, AB=4\)
The scale factor is the ratio of the lengths of a pair of corresponding sides. (image to preimage).
Thus, the scale factor is \(6/4=3/2\).
A bucket contains 1.34 hectoliters of water. How many centiliters of water are in the bucket? Use the metric table to
help answer the question.
Metric Table
unit
kilo-
1,000
hecto-
100
deka-
10
deci-
0.1
centi-
0.01
1
0.001
Answers
Answer:
the answer is C
Step-by-step explanation:
Answer: c) 13,400 centiliters
Step-by-step explanation: edge. 2022
the sum of squares of two consecutive odd numbers is 514 find the numbers
Answers
Correct Question : The sum of squares of two consecutive positive odd numbers is 514. Find the numbers.
\(\rule{130}1\)
Solution :
Let the two consecutive positive odd numbers be x and (x + 2)
\(\rule{130}1\)
☯ \(\underline{\boldsymbol{According\: to \:the\: Question\:now :}}\)
\(:\implies\sf x^2 + (x + 2)^{2} = 514 \\\\\\:\implies\sf x^2 + x^2 + 4x + 4 = 514\\\\\\:\implies\sf 2x^2 + 4x + 4 = 514 \\\\\\:\implies\sf 2x^2 + 4x = 514 - 4\\\\\\:\implies\sf 2x^2 + 4x = 510 \\\\\\:\implies\sf 2x^2 + 4x - 510 = 0\\\\\\:\implies\sf x^2 + 2x - 255 = 0 \:\:\:\:\:\Bigg\lgroup \bf{Dividing\:by\:2}\Bigg\rgroup\\\\\\:\implies\sf x^2 + 17x - 15x - 255 = 0\\\\\\:\implies\sf x(x + 17) - 15(x + 17) = 0\\\\\\:\implies\sf (x + 17) (x - 15)\\\\\\:\implies\sf x = - 17\:or\:x = 15\\\\\\:\implies\underline{\boxed {\sf x = 15}}\:\:\:\:\:\Bigg\lgroup \bf{Positive\:odd\: number}\Bigg\rgroup\)
When,
\(\bullet\: \textsf {x = } \textbf {15} \)
\(\bullet\: \sf x + 2 = 15 + 2 =\textbf{ 17} \)
\(\therefore\:\underline{\textsf{The required positive integer is \textbf{15 and 17}}}.\)
Circumference of 1/8th of a circle. There is 1/8 of a circle. The radius of the circle is 30 centimeters. The radius of the circle is 30 centimeters. Find the distance of the figure. Give steps
Answers
The circumference of 1/8th of a circle with a radius of 30 centimeters is 11.78 centimeters.
The formula for the circumference of a circle is C = 2πr, where C is the circumference, π is a mathematical constant approximately equal to 3.14, and r is the radius of the circle.
To find the circumference of 1/8th of a circle, we need to divide the circumference of the full circle by 8. So, the formula becomes:
C = (1/8) * 2πr
Substituting the given value of the radius, we get:
C = (1/8) * 2π(30)
Simplifying, we get:
C = (1/4) * π(30)
C = (1/4) * 30π
C = 7.5π
Approximating π as 3.14, we get:
C = 7.5 * 3.14
C = 23.55/2
C = 11.78
Therefore, the circumference of 1/8th of a circle with a radius of 30 centimeters is 11.78 centimeters.
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Complete Question:
Circumference of 1/8th of a circle. There is 1/8 of a circle. The radius of the circle is 30 centimeters. The radius of the circle is 30 centimeters. Find the distance of the figure. Give steps.
Find the mean and range of: 1.5, 0.5, 2, 3, 2.5
Answers
Answer:
mean 2 range2.5
Step-by-step explanation:
Richard's living room is 8 yards wide and 8 yards long. He wants to install pink carpet that costs $1.00 per square yard. How much will it cost to buy enough carpet for the living room?
PLEASEE HELLPPPP!
Answers
Area = Length x width
Area = 8 x 8 = 64 square yards
Total cost = area x cost per square yard
Total cost = 64 x 1.00 = $64
True/False
1) The nullspace of a 3x4 matrix cannot consist of only the zero vector.
2) The nullspace of a 4x3 matrix cannot consist of only the zero vector.
3) The set of all vectors of the form 1
x
y
where x and y range over all real numbers, is a subspace of R^3.
4) 3) The set of all vectors of the form 0
x
y
where x and y range over all real numbers, is a subspace of R^3.
Answers
Null space is defined as the set of vectors 'x' in Rn that are solutions to the matrix equation A*x = 0. False: The set of all vectors of the form 1 x y where x and y range over all real numbers is a subspace of R3. True: The set of all vectors of the form 0 x y where x and y range over all real numbers is not a subspace of R3.
1) False Null space can consist of zero vector only. A null space is defined as the set of vectors 'x' in R^n that are solutions to the matrix equation A*x = 0.
2) True The number of columns can never be less than the number of rows of the matrix in order for a null space to exist, hence a 4x3 matrix may have the null space of only the zero vector.
3) True The set of all vectors of the form 1 x y where x and y range over all real numbers, is a subspace of R^3. This set contains zero vector because for x=0 and y=0, we get the vector as [0,0,0]. Hence it is a subspace of R^3.
4) False The set of all vectors of the form 0 x y where x and y range over all real numbers, is not a subspace of R^3 as it doesn't contain zero vector. To have a subspace of R^3, it should contain a zero vector.
So, the correct options are:1) False2) True3) True4) False
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The indicated function y1(x) is a solution of the given differential equation. Use reduction of order or the formula y2=y1(x)∫e−∫P(x)dxy12(x)dx, as instructed, to find a second solution y2(x). y" + 2y' + y = 0 ; y1=xe−x
A) y2 =e^{-4x}
B) y2 =e^x
C) y2 =e^{-2x}
D) y2 =e^{-x}
Answers
To find a second solution, y2(x), for the given differential equation y" + 2y' + y = 0 using the reduction of order or the formula y2 = y1(x)∫e^(-∫P(x)dx)y1^2(x)dx, we will substitute the given solution y1(x) = xe^(-x) into the formula.
The second solution is y2(x) = e^(-2x) (Option C).
To explain the solution, let's start by substituting y1(x) = xe^(-x) into the formula for y2(x):
y2(x) = xe^(-x) ∫e^(-∫(2x)dx)(xe^(-x))^2dx
Simplifying the expression, we have:
y2(x) = xe^(-x) ∫e^(-2x)(x^2e^(-2x))dx
Integrating the expression inside the integral, we get:
y2(x) = xe^(-x) ∫(x^2e^(-4x))dx
Integrating this expression, we find:
y2(x) = xe^(-x) (-1/4) * (x^2e^(-4x) - 2∫xe^(-4x)dx)
Simplifying further, we have:
y2(x) = xe^(-x) (-1/4) * (x^2e^(-4x) - 2(-1/4)e^(-4x))
Finally, simplifying the expression, we obtain:
y2(x) = xe^(-x) (1/4) * (x^2e^(-4x) + (1/2)e^(-4x))
This can be further simplified as:
y2(x) = (1/4) * x^3e^(-5x) + (1/8) * xe^(-5x)
Therefore, the second solution is y2(x) = e^(-2x) (Option C).
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Solve the equation :- 3 - 2L = 13
Answers
Answer:
L = - 5Step-by-step explanation:
3 - 2L = 13
Subtract 3 from both sides
That's
3 - 3 - 2L = 13 - 3
- 2L = 10
Divide both sides by - 2
-2L / - 2 = 10 / - 2
L = - 5Hope this helps you
Answer: L = -8
Step-by-step explanation:
\(-3-2L=13\\\\Add(3)\\\\-2L=16\\\\Divide(-2)\\\\L=-8\)
Hope it helps <3
If there are infinite numbers of solutions of the two equations : x+4y=7 , 3X+ky = 21, then k =
Answers
Answer:
k = 12
Step-by-step explanation:
x + 4y = 7 ---------- (1)
3x + Ky = 21 -------- (2)
from equation 1
x = 7 - 4y
put the value of x in equation 2
3x + Ky = 21
3( 7 - 4y) + Ky = 21
21 - 12y + Ky = 21
Ky = 21 - 21 + 12y
Ky = 12y
divide both sides by y
k = 12
The value of the term k is equal to 12
We are given that there are infinite numbers of solutions of the two equations :
x + 4y = 7 ---------- (1)
3x + Ky = 21 -------- (2)
Then from equation 1
x = 7 - 4y
put the value of x in equation 2
3x + Ky = 21
3( 7 - 4y) + Ky = 21
21 - 12y + Ky = 21
Ky = 21 - 21 + 12y
Ky = 12y
Then divide both sides by y
k = 12
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Suppose x=2y-7. What is x if y=5
Answers
Answer:
x=3.Step-by-step explanation:
Given equation:
x=2y-7Given variables:
y=5x=?Simplify, then solve:
x=2y-7= x = (2 * 5) - 7= x = 10 - 7= 3x = 3.x=3
Step-by-step explanation:
x=2y-7 and y=5
x=2(5) - 7
multiply 5 by 2
x=10 - 7
substract 10 from 7
x=3
Pls help me on question 15
Answers
What is the equation of the ine perpendicular to 6x−2y=3 and passing through the point (5,−1)?
Answers
6x-2y=4xy
so this is the,correct answer your thinking of division
solve for x please hurry i will mark brainiest when it shows up if you answer correctly
Answers
The value of missing length x in the congruent triangles is determined as 3.6.
option D.
What is the length of segment of x?The length of segment x is calculated by applying congruency theorem as follows;
Consider triangle ABC,
AQ/AT = AB / AC
The given parameters include;
length AQ = 5
length AT = 6
length AB = 5 + 3 = 8
length AC = 6 + x
The value of missing length x is calculated as follows;
5/6 = 8/(6 + x )
5(6 + x) = 6(8)
30 + 5x = 48
5x = 48 - 30
5x = 18
x = 18/5
x = 3.6
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Which of the following is true?
Select the correct statement
Answers
Answer:
Top left
Step-by-step explanation:
Hello! I need help with this please thank you very much!
Answers
Answer:
plz explain >
Step-by-step explanation:
Which linear system has this matrix of constants? `[[12],[11],[4]]` Which answer option is correct A,B,C or D?????this is from a self-check activity
![Which linear system has this matrix of constants? `[[12],[11],[4]]` Which answer option is correct A,B,C](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/nXHSW3UITTduKsC9SvfIVeslCqtJjftv.png)
Answers
The given constants are 12,11 and 4
The matrix system has constants that can be written as follows:
\(ax+by+c=12\)\(dx+ey+fz=11\)\(gx+hy=iz=4\)Hence option D is correct.
PLEASE HELP ME WITH MY MATH HOMEWORK-
please answer questions 1 and 2
i also added a picture of a graph for the problem
Vue is a baseball player who hits a baseball through the air. The path the baseball takes after Vue hits it can be modeled by the graph below.
-
The baseball’s height above the ground in feet is a function of the time in seconds it travels through the air after it is hit. Use the graph to answer the following questions.
-
1. ) A point has been placed on the coordinate (3,144). What does this point mean in terms of the situation?
-
2. ) For what values of time(s) is the height of the ball decreasing?
Answers
Answer:
1.) The maximum height the ball reach thrown by Vue
Step-by-step explanation:
2.) 6 - 3 = 3
Pls help for final!!!
In the rectangle below, AC has a length of 28 units. What is the length of DE?
D
С
E
.
A
B
A. 56 units
B. 14 units
C. 21 units
D. 28 units
unts
Answers
Answer:
I think the right answer is 14.