# Spherical Boundary Displace Current

1. Nov 18, 2011

### superspartan9

1. The problem statement, all variables and given/known data

A current I is flowing along the y-axis and a
spherical surface with radius 1 m has its center at
origin, as in the figure left. A closed contour C is
chosen as in the figure, which is a boundary
between two semi-sphere surfaces S1 and S2. Based
on the uniqueness of magnetic field circulation (Closed line integral of)
H dot dl calculated from both surfaces S1 and S2,
find the total displacement current emanating from
the spherical surface using the Ampere’s law.

2. Relevant equations

No idea

3. The attempt at a solution

Not even sure where to start because it isn't clear whether these are conductive spheres or dielectric spheres. Once I figure that out, I could use the boundary conditions somehow... I honestly have no idea how to start this problem.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

#### Attached Files:

• ###### image.jpg
File size:
29.9 KB
Views:
83
2. Nov 19, 2011

### rude man

Well, maybe I can at least give you an idea or two.

First, current i must be time-varying, or nothing happens electric-field-wise.

Second: using Ampere, write an expression for B around the wire, including the space defined by the two hemispheres. BTW the hemispheres are just geometrically descriptive surfaces. They have no material meaning. Least that's what I assume.

Third: now you have B(x,y,z). What is the Maxwell relation that relates E to B?

Fourth: what is the relation between E and D? Assume non-conducting medium.

Fifth: What is the meaning of "displacement current emanating from the spherical surface", given D and the surfaces? Think of an analogy with how you get from conduction current density J to conduction current in the Maxwell relation relating B to J and D.

Sixth: how can you apply Stokes' theorem in conjunction with item 3 to calculate item five?

No guarantees her, maybe you'll discover something along the way I didn't.

Last edited: Nov 19, 2011