Electromagnetism question: Current flowing between concentric spheres

In summary, the question of current flowing between concentric spheres involves analyzing the electric and magnetic fields generated by a current-carrying conductor arranged in a spherical configuration. The problem typically requires application of concepts from electromagnetism, such as Gauss's law, to determine the distribution of current density, potential differences, and resulting electromagnetic fields within and around the spheres. Key considerations include the geometry of the spheres, the properties of the materials involved, and the nature of the current flow, which can influence the behavior of the electric and magnetic fields in the system.
  • #1
ka_reem13
4
0
Homework Statement
The space between two concentric, perfectly conducting spheres (radii ra < rb) is filled with a medium of conductivity σ. At t = 0, a charge q suddenly appears on the inner sphere. This charge is subsequently free to move by conduction.
(a) Calculate the current density in the medium between the spheres as a function of time for t > 0.
(b) Calculate the total heat generated due to this current.
(c) Calculate the reduction in electric field energy due to the charge redistribution. Comment on your results.
Relevant Equations
maxwells equations?
I know that my solution is time dependant, and I initially tried to use a capacitor model of sorts, but I realised as it was filled with a conductive medium, I cannot use a capacitor model. So now I am very stuck on this
 
Physics news on Phys.org
  • #2
Try working on a simpler version of the problem first, to start to get some intuition...

What if you have a flat plate capacitor with a resistor tied between the plates, and one of the plates gets a charge q placed on it? What is the equations for the current versus time through that resistor?

Then what kinds of changes should you make to account for the concentric sphere capacitor, and the varying resistance as a function of radial distance...?
 
  • #3
intuitively, it will be the same as discharging a regular capacitor through a resistor. However, instead of discharging to zero, it will discharge until both plates have equal and opposite charge? (Where this charge is q/2). Am I correct in saying this
 
  • #4
ka_reem13 said:
However, instead of discharging to zero, it will discharge until both plates have equal and opposite charge? (Where this charge is q/2). Am I correct in saying this
Discharging until q/2 is on each plate is not equal and opposite charges. What is the E field between the plates when they each have q/2 on them? :wink:
 

FAQ: Electromagnetism question: Current flowing between concentric spheres

What is the basic setup for studying current flowing between concentric spheres?

The basic setup involves two concentric spherical conductors, where the inner sphere has a radius \( r_1 \) and the outer sphere has a radius \( r_2 \). A potential difference is applied between the two spheres, causing a current to flow through the medium separating them, which is often assumed to be a dielectric material.

How do you calculate the electric field in the region between the concentric spheres?

The electric field \( E \) in the region between the concentric spheres can be determined using Gauss's Law. For a spherical shell of radius \( r \) (where \( r_1 < r < r_2 \)), the electric field is given by \( E = \frac{Q}{4 \pi \epsilon_0 r^2} \), where \( Q \) is the charge on the inner sphere and \( \epsilon_0 \) is the permittivity of free space.

What is the expression for the potential difference between the concentric spheres?

The potential difference \( V \) between the two spheres can be found by integrating the electric field from \( r_1 \) to \( r_2 \). The potential difference is given by \( V = \frac{Q}{4 \pi \epsilon_0} \left( \frac{1}{r_1} - \frac{1}{r_2} \right) \).

How do you determine the current flowing between the concentric spheres?

The current \( I \) flowing between the concentric spheres can be determined using Ohm's Law, \( I = V/R \), where \( V \) is the potential difference and \( R \) is the resistance of the medium between the spheres. The resistance \( R \) can be calculated by considering the geometry and the resistivity \( \rho \) of the material, leading to \( R = \frac{\rho}{4 \pi} \left( \frac{1}{r_1} - \frac{1}{r_2} \right) \).

What are some practical applications of studying current flow between concentric spheres?

Understanding current flow between concentric spheres has applications in various fields such as geophysics (e.g., modeling the Earth's electric field), medical imaging (e.g., spherical electrodes in bioelectric measurements), and the design of spherical capacitors and other spherical electronic components.

Similar threads

Why can we model spherical capacitor with two dielectrics as two capacitors in series?
Replies
4
Views
1K
What explains the current flow in a LC circuit?
Replies
4
Views
1K
Gauss' Theorem - Net Flux Out - Comparing two vector Fields
Replies
5
Views
1K
Understanding the meaning of "expected fraction" (Statistics)
Replies
4
Views
2K
I Does a Railgun's Current Violate Conservation of Momentum?
2
Replies
61
Views
4K
Can I use individual capacitor IR for parallel circuit balancing resistors?
Replies
3
Views
1K
RC Circuit current through capacitor question
Replies
1
Views
1K
Capacitor Questions Charging and Discharging
Replies
4
Views
2K
Electrical How to use capacitors in a Solenoid circuit
Replies
32
Views
7K
Two concentric conducting spherical shells and resistor in between
2
Replies
44
Views
3K

Hot Threads

Recent Insights

Back
Top