20115ee1_1_HW1 Solutions

# 20115ee1_1_HW1 Solutions - HW1 Solution 2.2. The force...

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: HW1 Solution 2.2. The force exerted on will be The force exerted on will be Where , And the magnitude Unit vector , Since 2.4. , z P(a,a,a) a y x The total vector force will be 2.5. (a)If where Also So , find E at P3(1,2,3) and . (b) At what point on the y axis is Ex = 0? P3 is now at (0, y, 0), so Also Now the x component of E at the new P3 will be: . To obtain Ex = 0, we require the expression in the large brackets to be zero. This expression simplifies to the following quadratic: Which yields the two values: y=-6.89, -22.11 2.7. A 2μC point charge is located at A(4, 3, 5) in free space. Find Eρ, Eφ, and Ez at P(8, 12, 2). Then, at point P, Now, , And Finally, 2.9. A 100 nC point charge is located at A(− 1, 3) in free space. 1, a) Find the locus of all points P(x, y, z) at which Ex = 500 V/m: The total field at P will be: where and where 2]1/2. The x component of the field will be And so our condition becomes: b) Find from which if P(− 2, , 3) lies on that locus: At point P, the condition of part a) becomes 0.47, or = 1.69 or 0.31 2.11. A charge Q0 located at the origin in free space produces a field for which Ez = 1 kV/m at point P(−2, 1,−1). a) Find Q0: The field at P will be Since the z component is of value 1kV/m, we find b) Find E at M(1, 6, 5) in cartesian coordinates: Or c) Find E at M(1, 6, 5) in cylindrical coordinates: At M, Now so that d) Find E at M(1, 6, 5) in spherical coordinates: At M, the carge is at the origin, we expect to obtain only a radial component of Since . This will be: 2.13. A uniform volume charge density of 0.2μC/m3 is present throughout the spherical shell extending from r = 3 cm to r = 5 cm. If ρv = 0 elsewhere: a) find the total charge present throughout the shell: This will be b) find r1 if half the total charge is located in the region 3 cm < r < r1: If the integral over r in part a) is taken to r1, we would obtain Thus ...
View Full Document

## This note was uploaded on 12/05/2011 for the course EL ENGR 1 taught by Professor Joshi,chand during the Fall '11 term at UCLA.

Ask a homework question - tutors are online