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Current density is given in cylindrical coordinates as j = -1067¹.5 A/m² in the region 0

Current density is given in cylindrical coordinates as j = -1067¹.5 A/m² in the region 0

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electromagnetic field)I want a detailed solution because my teacher changes the numbers. I want a detailed solution. Understand the solution
• Current density is given in cylindrical coordinates as j = -1067¹.5 A/m² in the region 0 <p ≤ 20 μm; for p≥ 20 μm, j = 0. a. Find the total current crossing the surface=0.1 m in the direction. b. If the charge velocity is 2×106 m/s at := 0.1 m, find p, there. c. If the volume charge density at = 0.15 m is-2000 C/m³, find the charge velocity there. A- Total current is calculated by. J* ((p1)² - (p0)²) * 2π * ¢dza. Where J = Density = -10^6 * z^1.5 p1 = Upper bound of p = 20 p0= Lower bound of p = 0 π = 22/7 dza = 10^-6 z = 0.1 Total current = -10^6 * z^1.5 = 10^6 * 0.1^1.5 = -39.7543477278310 = -39.8μA B. Calculating velocity charge density at (pv) Density (J) = pv * V Where J = Density = -10^6 * z^1.5 V = 2*10^6 z = 0.1 (202-0²) * 2 * 22/7 10^-6 (202-02) * 2 * 22/7 * 10^-6 Substitute the above values -10^6 * 0.1 ^1.5 = pv * 2*10^6 pv = (-10^6 * 0.1^1.5)/(2*10^6) pv = -0.1^1.5/(2) pv = -0.015811388300841 pv = -0.01581 Approximated pv=-15.81mC/m³ C. Calculating Velocity Velocity = J/V Where Velocity Charge Density=-2000 C/m3 Where J = -10^6* z^1.5 z = 0.15 J=-10^6 * 0.15^1.5 J = -58094.75019311125 Velocity = -58094.75019311125/-2000 Velocity = 29.047375096555625m/s Velocity = 29.05m/s
Transcribed Image Text:• Current density is given in cylindrical coordinates as j = -1067¹.5 A/m² in the region 0 <p ≤ 20 μm; for p≥ 20 μm, j = 0. a. Find the total current crossing the surface=0.1 m in the direction. b. If the charge velocity is 2×106 m/s at := 0.1 m, find p, there. c. If the volume charge density at = 0.15 m is-2000 C/m³, find the charge velocity there. A- Total current is calculated by. J* ((p1)² - (p0)²) * 2π * ¢dza. Where J = Density = -10^6 * z^1.5 p1 = Upper bound of p = 20 p0= Lower bound of p = 0 π = 22/7 dza = 10^-6 z = 0.1 Total current = -10^6 * z^1.5 = 10^6 * 0.1^1.5 = -39.7543477278310 = -39.8μA B. Calculating velocity charge density at (pv) Density (J) = pv * V Where J = Density = -10^6 * z^1.5 V = 2*10^6 z = 0.1 (202-0²) * 2 * 22/7 10^-6 (202-02) * 2 * 22/7 * 10^-6 Substitute the above values -10^6 * 0.1 ^1.5 = pv * 2*10^6 pv = (-10^6 * 0.1^1.5)/(2*10^6) pv = -0.1^1.5/(2) pv = -0.015811388300841 pv = -0.01581 Approximated pv=-15.81mC/m³ C. Calculating Velocity Velocity = J/V Where Velocity Charge Density=-2000 C/m3 Where J = -10^6* z^1.5 z = 0.15 J=-10^6 * 0.15^1.5 J = -58094.75019311125 Velocity = -58094.75019311125/-2000 Velocity = 29.047375096555625m/s Velocity = 29.05m/s
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