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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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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