This picture represents the field lines of a single positive point charge.
What is the divergence in the boxed region? What is the divergence of the whole field?
Boxed region is zero; whole field is zero
Boxed region is non-zero; whole field is zero
Boxed region is zero; whole field is non-zero
Boxed region is non-zero; whole field is non-zero
???
Notes from HW 2 (From Bryan)
To get full credit:
Make sure to explain your answers when asked
For graphs, make sure to annotate them well
Remember that approximations are not what value but how it gets there
Activity: For a the electric field of a point charge, E(r)=14πε0qr2ˆr, compute ∇⋅E.
Hint: The front fly leaf of Griffiths suggests that the we take:1r2∂∂r(r2Er)
Remember this?
What is the value of:
∫∞−∞x2δ(x−2)dx
0
2
4
∞
Something else
Activity: Compute the following integrals. Note anything special you had to do.
Row 1-2: ∫∞−∞xexδ(x−1)dx
Row 3-4: ∫−∞∞log(x)δ(x−2)dx
Row 5-6: ∫0−∞xexδ(x−1)dx
Row 6+: ∫∞−∞(x+1)2δ(4x)dx
Compute:
∫∞−∞x2δ(3x+5)dx
25/3
−5/3
25/27
25/9
Something else
A point charge (q) is located at position R, as shown. What is ρ(r), the charge density in all space?
ρ(r)=qδ3(R)
ρ(r)=qδ3(r)
ρ(r)=qδ3(R−r)
ρ(r)=qδ3(r−R)
Something else??
What are the units of δ(x) if x is measured in meters?
δ(x) is dimension less (‘no units’)
[m]: Unit of length
[m2]: Unit of length squared
[m−1]: 1 / (unit of length)
[m−2]: 1 / (unit of length squared)
What are the units of δ3(r) if the components of r are measured in meters?
[m]: Unit of length
[m2]: Unit of length squared
[m−1]: 1 / (unit of length)
[m−2]: 1 / (unit of length squared)
None of these.
What is the divergence in the boxed region?
Zero
Not zero
???
We have shown twice that ∇⋅E=0 using what seem to be appropriate vector identities. But physically, ∇⋅E=ρ/ε0. What is going on?!
We broke physics - let's call it a day
There's some trick to get out of this and that makes me uncomfortable
I can see what we need to do
???
This picture represents the field lines of a single positive point charge.
What is the divergence in the boxed region? What is the divergence of the whole field?
Boxed region is zero; whole field is zero
Boxed region is non-zero; whole field is zero
Boxed region is zero; whole field is non-zero
Boxed region is non-zero; whole field is non-zero
???
CORRECT ANSWER: C