Assignment: EMT
Question 1:
The value of Eat P(ρ = 2,φ = 40o,z = 3) is given as = 100aρ- 200aφ + 300azV/m. Determine the incremental work required to move a20 μC charge a distance of 6μm:
a. in the direction of aρ;
b. in thedirection of aφ;
c. in the direction of az;
d. in the direction of E;
e. in thedirection of G = 2ax - 3ay + 4az.
Question 2:
If E = 120aρV/m, find the incremental amount of work done in movinga 50μC charge a distance of 2 mm from
a. P(1,2,3) toward Q(2,1,4);
b. Q(2,1,4)toward P(1,2,3).
Question 3:
Compute the value of∫_A^P G• dL for G = 2ya_xwith A(1,-1,2) andP(2, 1, 2) using the path
a. straight-line segments A(1,-1,2) to B(1,1,2)to P(2,1,2);
b. straight-line segments A(1,-1,2) to C(2,-1,2) toP(2,1,2).
Question 4:
Let G = 3xy2ax + 2zayGiven an initial point P(2,1,1) and a final pointQ(4,3,1),find∫G• dL using the path
a. straight line: y = x - 1,z = 1;
b. parabola: 6y = x^2+ 2,z = 1.
Question 5:
Given the current density J = -10^4 [sin(2x)e^(-2y) ax + cos(2x)e^(-2y) ay ] kA/m^2
a. Find the total current crossing the plane y = 1 in the ay direction in the region 0 b. Find the total current leaving the region 0
Repeat part (b), but use the divergence theorem.
Question 6:
Let J = 400 sin θ/(r^2+ 4) ar A/m^2.
a. Find the total current flowing through that portion of the spherical surface r = 0.8, bounded by 0.1π < θ <0.3π,0 < φ <2π.
b. Find the average value of J over the defined area.
Question 7:
The current density in a certain region is approximated by=(0.1/r)exp(-10^6 t) a_r A/m^2 in spherical coordinates.
a. At t=1μs, how much current is crossing the surface r=5?
b. Repeat for r=6
c. Use the continuity equation to find ρ_v (r,t) assuming that ρ_v→0as t→∞.
d. Find an expression for the velocity of the charge density.
Question 8:
Two perfectly conducting cylindrical surfaces of lengthl are located at ρ = 3 and ρ = 5 cm. The total current passing radially outward through the medium between the cylinders is 3 A dc.
Find the voltage and resistance between the cylinders, and E in the region between the cylinders, if aconducting material having σ = 0.05 S/m is present for 3 < ρ <5 cm.