# Spherical Boundary Displace Current

## Homework Statement

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.

No idea

## 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.

## The Attempt at a Solution

#### Attachments

• image.jpg
29.9 KB · Views: 370

## Answers and Replies

rude man
Homework Helper
Gold Member
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: