Spherical Boundary Displace Current

• superspartan9
In summary, the problem involves finding the total displacement current emanating from a spherical surface with a radius of 1 m, centered at the origin, using the uniqueness of magnetic field circulation and Ampere's law. The current must be time-varying and the spheres are assumed to be non-conducting. The problem involves using the Maxwell relation to relate E to B and then using Stokes' theorem to calculate the displacement current.
superspartan9

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.

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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:

1. What is Spherical Boundary Displace Current?

Spherical Boundary Displace Current, also known as SBDC, is a phenomenon that occurs when a charged particle moves near a spherical boundary. The electrical charge of the particle causes a displacement of charge along the surface of the boundary, resulting in a current flow.

2. How is SBDC different from regular displacement current?

SBDC differs from regular displacement current in that it occurs specifically at a spherical boundary. Regular displacement current occurs in any situation where there is a changing electric field, whereas SBDC only occurs when a charged particle moves near a spherical boundary.

3. What are the applications of SBDC?

SBDC has various applications in physics and engineering. It is used in the design of antennas, as well as in the study of electromagnetic waves and quantum mechanics. It also has applications in medical imaging, such as in MRI machines.

4. How is SBDC related to the concept of capacitance?

SBDC is closely related to the concept of capacitance. In fact, the displacement current at a spherical boundary can be thought of as the flow of charge that is responsible for the capacitance of the boundary. The larger the capacitance, the more charge is displaced and the stronger the SBDC.

5. Can SBDC be observed in everyday life?

SBDC is not typically observed in everyday life, as it requires specific conditions to occur. However, it is a fundamental concept in electromagnetism and is used in various technologies that we encounter daily, such as in wireless communication and medical imaging.

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