What is Displacement current: Definition and 53 Discussions
In electromagnetism, displacement current density is the quantity ∂D/∂t appearing in Maxwell's equations that is defined in terms of the rate of change of D, the electric displacement field. Displacement current density has the same units as electric current density, and it is a source of the magnetic field just as actual current is. However it is not an electric current of moving charges, but a time-varying electric field. In physical materials (as opposed to vacuum), there is also a contribution from the slight motion of charges bound in atoms, called dielectric polarization.
The idea was conceived by James Clerk Maxwell in his 1861 paper On Physical Lines of Force, Part III in connection with the displacement of electric particles in a dielectric medium. Maxwell added displacement current to the electric current term in Ampère's Circuital Law. In his 1865 paper A Dynamical Theory of the Electromagnetic Field Maxwell used this amended version of Ampère's Circuital Law to derive the electromagnetic wave equation. This derivation is now generally accepted as a historical landmark in physics by virtue of uniting electricity, magnetism and optics into one single unified theory. The displacement current term is now seen as a crucial addition that completed Maxwell's equations and is necessary to explain many phenomena, most particularly the existence of electromagnetic waves.
If so, what will I measure in the Ampermeter, the zero total current or the value of the conduction current?
I was thinking of the following example- a circuit consist of a current source, an Ampermeter, a switch, and a semiconductor. The semiconductor can have both conduction and displacement...
I was thinking of a standard, high school level discussion of the displacement current. The need for introducing this quantity is demonstrated by considering a circuit with a charging capacitor, and (for the sake of simplicity) a circular loop whose axis is along the (straight) wire carrying the...
I’m self taught so I have a lot of holes in my understanding. I also have little to no mathematical understanding. Even though ironically, I tend to prefer to picture electricity as numbers rather than “water” in a pipe, etc.
I’ve been studying displacement current recently and have a question...
The Biot-Savart law which describes a magnetic field created by a displacement current: $$\frac{dB}{dV}=\frac{\mu_0\epsilon_0}{4\pi}\frac{\frac{∂E}{∂t}×r}{r^2}$$
What's the relativistically co-variant form of this equation?
Is the introduction of speed of light propagation delays enough, or...
We all know a moving charge generates a magnetic field.
A moving charge also generates a displacement current ∂E/∂t.
Is the magnetic field generated entirely due to the presence of the displacement current, or is there an independent, separate effect which contributes to the magnetic field?
To put this in another way, is there some reason from first-principles as to why we have j as the spatial component of the four-current rather than the total current density which includes the displacement current? Has anyone tried to see what the experimental consequences of this would be?
Kevin M.
I had a question in my textbook asking why is the magnetic field generated by the displacement current in a capacitor more difficult to be measured than the magnetic field generated by the current in the wire. But I don't know how is this type of magnetic field measured, I only know that they...
Homework Statement
A wire with conductivity σ carries current I. The current is increasing at the rate dI/dt. Show that there is a displacement current in the wire equal to e0/σ⋅dI/dt
Homework Equations
Id = e0⋅dφ/dt
dφ/dt = dE/dt ⋅ A (This is usually true, I'm not sure if it's useful in...
To calculate the displacement current in a coaxial cable (with equal and opposite currents on the inner and outer conductors), most standard texts use the magnetoquasistatic approximation, which ignores the time-varying electric field term in Ampere’s Law.
Using this approximation, the...
Homework Statement
A capacitor is made of two parallel plates of area A, separation d. It is being charged by an AC source. Show that the displacement current inside the capacitor is the same as the conduction current.
Homework Equations
Idisp = ε(dΦE/dt)
Q = CV
C = Aε/d
Xc = 1/(2πƒC)
Q(t)...
I have a doubt on this calculation of magnetic field in presence of displacement current. Consider a capacitor of radius ##R## and with plates at distance ##d## being charged: there is a displacement current in it.
Suppose that I want to calculate the magnetic field ##B## at a distance ##r <...
Please help me with this. I am having a hard time understanding the role of displacement currents in a circus. The common knowledge is actual current is the movement of electron in a circus. Now, if there is a gap and an AC source, there would be an electric displacement field and a displacement...
Dynamos and transformers have inductor coils reacting with changing magnetic fields and importing energy into the circuit in form of induced current
1. What about the counterpart of above principle in case of capacitors?
2. Will capacitors interact with...
1. The problem statement,
A capacitor is there in free space consisting of 2 circular plates of radius ##r## separated by a distance ##z## which is a function of time. ##z(t) = z_0 + z_1 cos (\omega t)##; ##z_0(<<r)## and ##z_1(<z_0)## are constants. The separation ##z(t)## is varied in such a...
The figure shows two insulated metal electrodes kept in pure water with a small gap between them.
When sufficiently large voltage pulses applied between electrodes, there is a flow of displacement current through the insulators and water, but will this split the water molecules because of the...
Homework Statement
A long straight wire has a line charge, λ that varies in time according to: λ = λ0e(-βt). A square loop of dimension, a, is adjacent to the wire (at a distance a away from the wire). Calculate expressions for the displacement current at the center of the wire loop and the...
1. In above image an insulated metal plate has been placed inside Earth (soil), and an voltage is applied between plate and Earth groung what will be the capacitance here??
2. one plate is the metal and the other plate is entire earth, so it is a big assymetrical Capacitor or What?
all...
Homework Statement
A long, straight wire has a line charge, λ, that varies in time according to: λ = λ0 exp(-βt). A square wire loop of dimension a is located adjacent to the wire at a distance of a from the wire. Calculate expressions for the displacement current at the center of the wire loop...
Homework Statement
Show that the conduction and displacement currents cancel each other for a spherical radioactive solid emitting charged particles radially outwards
Homework Equations
Maxwell's equations
Current density (j)
Displacement current density (jd)
The Attempt at a Solution
I...
A parallel plate capacitor with circular plates of radius R is being discharged. The displacement current of discharge through a central circular area, parallel to the plates and with radius R/2, is 2.0 A. What is the discharging current?
We know that the so-called displacement current is defined as
$$i_d=\varepsilon_0 \, \frac{\partial\Phi_e}{\partial t}.$$
Like regular current which is the movement of charges, $i_d$ has a direction, even though it's technically a scalar. How do we find its direction?
I guess i have discovered or i may say re-discovered if already existing a formula for the resistance offered to the displacement current in capacitors.
I am not talking about the capacitive reactance but, a resistance which depends on time, area and further more calculations.
What shall i do...
Dear All,
I have a doubt whether galvanometer detects displacement currents due to time varying electric field or not?please let me know,if anybody have an idea about this.
Regards
Arvind
Homework Statement
The problem is #1 given here:
http://ocw.mit.edu/courses/physics/8-311-electromagnetic-theory-spring-2004/assignments/ps1.pdf
And there is a solution publicly available here...
Homework Statement
Displacement current arises due to
a)changing electric field
b)changing magnetic field
c)both
Homework Equations
The Attempt at a Solution
I think the answer should be c) because we already know that changing electric field is responsible for displacement current...
So, consider an average shorted capacitor connected to an alternating current power source. This capacitor has a certain capacitance, voltage, displacement current, etc. associated with it. Assume the dielectric of this capacitor is air. Let us increase the frequency of this source. Recall that...
Homework Statement
If electric flux density (D) is given by the vector (xy,yz,xz) then calculate the displacement current density
Homework Equations
Jd = dD/dt
The Attempt at a Solution
if you differentiate D, in terms of t, then you just get 0..but that apparently isn't the answer
Homework Statement
I am having trouble grasping why exactly displacement current and conduction current are sometimes equal to each other and sometimes are not.
My textbook states that the displacement current is defined as ε0 * d(EA)/dt. That is, epsilon not times change in electric flux. I...
I know and fully understand the mathematical definition of it. But what's the physical explanation? Is it something like "preservation of current" or something?
Homework Statement
a capacitor of capacitance 'C' is being charged across a dc source with an ammeter . will the ammeter show a momentary deflection during the process of charging? if so, how would it and the resulting continuity of current in the circuit be explained ?
Homework Equations...
You have a spherical capacitor with inner conductor radius a and outer conductor with radius b. The capacitor is filled with a perfect homogeneous dielectric of permittivity ε and is connected to a low-frequency time-harmonic voltage v(t)=V_{0}cos(ωt). Find the displacement current density...
Hi All,
Consider a situation in which a coaxial cable have electric current i(t) = Imax * cos(w*t) flowing through its cilindrical inner cylindrical core (with radius a) and the inverse current flowing on its surface cover (with radius b).
I would like to know if it is correct to say that...
OK, I was thinking about transformers and mutual induction and then drifted onto displacement current. I then decided to build a simple test apparatus and test for the magnetic field between two parallel plates. using a variety of coil designs to have as much of the windings perpendicular to the...
"Qausi-static" displacement current (Purcell)
Hello all,
On page 329, chapter 9 of Purcell's E&M book, he describes why the "displacement current" produces nearly zero magnetic field for slowly varying fields. By taking the curl of the displacement current Jd, he shows that...
Hello,
I'm new on this forum. I hope I could help some of you next days. But today I have a question for you.
I have a geophysics oral exam on wednesday.
The course material is not clear, and I don't understand the wikipedia pages.
What is the physical difference between displacement current...
Homework Statement
For copper we find that J=\sigmaE , where \sigma has the value 5.8x10^7 mksc units. If an alternating electric field represented by E0ei\omegat exists within the copper. Find the ratio of the conduction to the displacement current density at a frequency of 1megacycle/sec...
Hi
I have already solved the problem. I just have some doubts about the solution given in the
solution manual. This is "Physics for scientists and engineers" by Serway, Jewett
In the solution for part b) , the author has taken the area of whole Amperian loop while
calculating the electric...
Homework Statement
conductivity=1/100 siemens/meter
epsilon=3*epsilon[0]
at which frequency displacement current is equal to conduction current?
Homework Equations
The conduction current is LaTeX Code: I =C * \\frac {dV}{dt}
The displacement current D can be calculated from...
Homework Statement
A 0.1[A] current is charging a capacitor that has square plates 5cm on each side. The plate separation is 4mm. Find (a) the time rate of change of the electric flux between the plates and (b) the displacement current between the plates.
The Attempt at a Solution
So I had...
Hi, just to check which equation for Jd (the displacement current density) is correct:
1) Jd = ε0εr(dE/dt), or
2) Jd = ε0(εr-1)(dE/dt)
1) came from the fact that Jd = ε(dE/dt) and ε=ε0εr
2) came from differentiating P = ε0(εr-1)E (since Jd=dP/dt).
It's only a minor thing but in a...
Is there really a magnetic field around a capacitors (parallel plate) in vacuum dielectric fed by a variable voltage? Is there an experiment that can prove that we don't need actually a moving electrical charge to create a magnetic field, but a variable electric field in vacuum its enough?
Does anyone know how to solve or at least how to begin solving the following problem?:
Prove that displacement current in the Maxwell equations can be neglected if characteristic time τ of changing electromagnetic field in the system satisfies to the following condition: τ >> L/c where L is...
Recently, I came across an interesting debate over the meaning of Maxwell’s “displacement current.” I wonder if you are familiar with this debate and if so what is your position? On the internet, you can find a paper on this topic by Nigel Cook here:
http://www.wbabin.net/physics/cook.htm"...
When Maxwell first described the displacement current, he rationalized it with imagining space filled with ether. We now know that ether does not exist. So the question remains what is the rationalization behind displacement current?
Wikipedia states "... It is now believed that...
Hi, just out of curiosity...
Ampere's Law describes that an electric current produces a magnetic field. When corrected with Maxwell's displacement current, it describes that a magnetic field is also created by a time-varying electric field.
Does this mean that an electric current produces...
Homework Statement
A parallel-plate, air-filled capacitor is being charged. The circular plates have radius 4.00 cm, and at a particular instant the conduction current in the wires is 0.280 A. (a) What is the displacement current density jD in the air space between the plates? (b) What is...
Homework Statement
Use an integral form of the Gauss law to show how the magnitude of D inside the capacitor depends on the charge on the plates of a parallel plate capacitor and their area.
Homework Equations
Gauss
\int{E.nda}=\frac{\rho}{\epsilon_{0}}
\nabla.D=\rho
where div...
Hello guys. I gave this one the good ol effort and seem to have gotten stuck. Can anyone help?
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A copper wire with a circular cross-section area of 1.5 mm2 carries a current of 11 A. The resistivity of the material is 2.1 × 10-8 ·m. a) What is the uniform electric field in the...
I have a question in regards to displacement current. Is this theory mainly used to describe the field when a capacitor has a shape other than a flat one?
Can anyone link me a site that clearly explains how we can use the concept of displacement current?
From what I understand through...