Chapter 4.2, Problem 4.11P

Evaluate the line integral, where C is the given curve. Sc (x + yz)dx + 2x dy + xyz dz C consists of line segments from (1, 0, 1) to (2, 2, 1) and from (2, 2, 1) to (2, 4, 3). The force exerted by an electric charge at the origin on a charged particle at a point (x, y, z) with position vector r = is F(r) = Kr/1r|³ where K is a constant. Find the work done as the particle moves along a straight line from (5, 0, 0) to (5, 1, 5). Find the mass and center of mass of a wire in the shape of the helix x=t, y = 5cos(t), z = 5sin(t), 0 st ≤ 2π, if the density at any point is equal to the square of the distance from the origin. (mass) ) (center of mass)

The axis of a long dielectric tube with an inner radius r = 2m and an outer radius r = 5m coincides with the z-axis. Inside the dielectric body, there is a polarization vector in the form of P = P.(3yâx + 4xây). Find the equivalent volume charge density Ppv at point (2,0,4). Ppv = 0 O A) O, Ppv 7Por sin ø cos Ø %3D B) Ppv Por sin ø cos Ø

Question 2 a. Electrostatic fields have many applications, but most are low “low-power" applications; that is relatively low forces are involved. Explain why this is so. b. Given that D= (10ră ) ar (c/m²) in cylindrical coordinates, evaluate both sides of the divergence theorem for the volume enclosed by r= Im, r= 2m and Z= 0 and Z= 10

1.27| The important dipole field (to be addressed in Chapter 4) is expressed in spherical coordinates as E =4 (2 cos 0 a, + sin 0 ag) where A is a constant, and where r> 0. See Figure 4.9 for a sketch. (a) Identify the surface on which the field is entirely perpendicular to the xy plane and express the field on that surface in cylindrical coordinates. (b) Identify the coordinate axis on which the field is entirely perpendicular to the xy plane and express the field there in cylindrical coordinates. (c) Specify the surface on which the field is entirely parallel to the xy plane.

Uniform line charges of 134 nC/m lie along the entire extent of the three coordinate axes. Assuming free space conditions, find Ey at P(5, -3,7).

ELECTROMAGNETICS: Coulomb's Law and Electrical Field Intensity 5. An infinite uniform line charge, pi = 2 nC/m, lies alone the x -axis in free space, while point charges of 8 nC are located at (0,0, 1) and (0,0, –1) a. Find E at (2, 3, -4) b. To what value should på be changed to cause E to be zero at (0, 0, 3)?

Consider the vector field ʊ(r) = (x² + y²)êx + (x² + y²)êy + z²êz. Decompose the vector field (r) into the sum of two other vector fields, a (r) and 5(r), such that a(r) has no divergence (it is solenoidal) and 5 (r) has no curl (it is irrotational). The answer is not unique. This is the Helmholtz decomposition.

Which of the following integrals will give the correct value for the total charge of an L-shaped wire carrying a line charge density of sin(x)cos(y) coulombs per meter? The L-shaped wire lies on the plane z = 3 m. It is composed of two wires: one extending from (2, 1, 3) m to (5, 1, 3) m and another extending from (5, 1, 3) m to (5, 3, 3) m. .5 sin(x)cos(y) dx dy I sin(x)cos(y) dx dy cos(1) sin(x) dx + sin(2) cos(y) dy cos(1) / sin(x) dx + sin(5) [ cos(y) dy