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horrorfan
22 days ago
13

Current density is given in cylindrical coordinates as J = −106z1.5az A/m2 in the region 0 ≤ rho ≤ 20 µm; for rho ≥ 20 µm, J = 0

. (a) Find the total current crossing the surface z = 0.1 m in the az direction. (b) If the charge velocity is 2 × 106 m/s at z = 0.1 m, find rhoν there. (c) If the volume charge density at z = 0.15 m is −2000 C/m3, find the charge velocity there.
Engineering
1 answer:
Mrrafil [253]22 days ago
8 0
a. Total current yields -39.8μA. b. The value of ρν at z = 0.1 m is -15.81mC/m³. c. The charge velocity at z = 0.15 m is calculated to be 29.05m/s. To explain further: Total current is computed as follows: Using the formula J * ½((ρ1)² - (ρ0)²) * 2 π * φdza, where J represents Density = -10^6 * z^1.5, with ρ1 as 20 (upper limit for ρ), ρ0 as 0 (lower limit for ρ), π approximated as 22/7, and φdza as 10^-6, considering z = 0.1: The overall current then becomes: = -10^6 * z^1.5 * ½(20² - 0²) * 2 * 22/7 * 10^-6, = 10^6 * 0.1^1.5 * ½(20² - 0²) * 2 * 22/7 * 10^-6, which resolves to approximately -39.8μA. b. To derive the charge density velocity (ρv): Density (J) = ρv * V, where J remains the same as before, V is noted to be 2 * 10^6, within the context of z = 0.1: Substituting generates -10^6 * 0.1 ^1.5 = ρv * 2 * 10^6, from which it follows that ρv = (-10^6 * 0.1^1.5)/(2 * 10^6), leading to the final computation of ρv = -0.01581mC/m³. c. To evaluate velocity at z = 0.15: Velocity is computed as J/V: Given that the volume charge density amounts to -2000 C/m³, J at this height calculates to -10^6 * 0.15^1.5: Thus, Velocity = -58094.75019311125/-2000, which results in approximately 29.05m/s.
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  2. user_input = input("Enter number of rows and columns: ")
  3. myArr = user_input.split(" ")
  4. num_rows = int(myArr[0])
  5. num_cols = int(myArr[1])
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  7. for i in range(num_rows):
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  9. for j in range(num_cols):
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  12. output = ""
  13. for i in range(len(seats)):
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  15. output += str(i + 1) + seats[i][j] + " "
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Explanation:

Initially, we create a small list of alphabets from A to J (Line 1).

We then request the user to enter the number of rows and columns (Line 3). Given that the input comes as a string (e.g., "2 3"), we utilize the split() method to separate the numbers into individual items in a list (Line 4). The first item (row number) is assigned to variable num_rows, while the second item (column number) goes to num_cols.

Subsequently, we construct the seats list with a nested for-loop (Lines 10-15). Once the seats list is formed, another nested for-loop generates the required output string as per the question (Lines 19-21).

Finally, the output is printed (Line 23). For example, an input of 2 3 results in the output:

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