Average Electric Field

Electricity and Magnetism Level 4

There is a fixed volume of sphere having equation x 2 + y 2 + z 2 ≤ 1 x^{2}+y^{2}+z^{2}≤1 .A charge ( q = + 10 C ) (q=+10C) is placed at a random position in this volume. Calculate the magnitude of E a v e r a g e E_{average} field produced by it in ( 2 , 0 , 0 ) (2, 0,0) .
Details and Assumptions
1 ) ϵ 0 = 1 1)\epsilon_{0}=1
The problem is purely original.


The answer is 0.210.

A Former Brilliant Member by A Former Brilliant Member

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Steven Chase
May 3, 2020

I assume that we are averaging the field magnitude, and not taking the magnitude of the average vector field. These two are not necessarily the same thing. I did the work in spherical coordinates. 

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
 
import math

Num = 200

R = 1.0
q = 10.0

x0 = 2.0
y0 = 0.0
z0 = 0.0

e0 = 1.0
k = 1.0/(4.0*math.pi*e0)

##################################

dr = R/Num
dtheta = 2.0*math.pi/Num
dphi = math.pi/Num

##################################

Eav = 0.0
V = 0.0

r = 0.0

while r <= R:

    theta = 0.0

    while theta <= 2.0*math.pi:

        phi = 0.0

        while phi <= math.pi:

            x = r*math.cos(theta)*math.sin(phi)
            y = r*math.sin(theta)*math.sin(phi)
            z = r*math.cos(phi)

            Dx = x - x0
            Dy = y - y0
            Dz = z - z0

            Dsq = Dx**2.0 + Dy**2.0 + Dz**2.0

            E = k*q/Dsq

            dV = (r**2.0)*math.sin(phi) * dr * dtheta * dphi
            V = V + dV

            Eav = Eav + E*dV

            phi = phi + dphi

        theta = theta + dtheta

    r = r + dr

##################################

Eav = Eav / V

print Num
print Eav


#>>> 
#100
#0.211875765966
#>>> ================================ RESTART ================================
#>>> 
#200
#0.21101241899
#>>>

2 Helpful 2 Interesting 2 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...