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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.
So , find E at P3(1,2,3) and
At what point on the y axis is Ex = 0? P3 is now at (0, y, 0), so
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
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.
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
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:
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 ...
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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.
- Fall '11