Imagine a wire with current I flowing through it. If we take a closed loop that doesnt contain the I the line integral will be zero. Does this means magnetic field is zero ? Also does Ampere law calculating the total magnetic field or only the sum of magnetic fields from the currents that are enclosed in the loop?
120745
Let’s say we have a current wire with a current $I$ flowing. We know there is a field of $B=\frac{\mu_0I}{2\pi r}$ by using , and a simple integration path which goes circularly around the wire. Now if we take the path of integration as so the surface spans doesn’t intercept the wire we trivially get a $B=0$ which is obviously incorrect.  I see that I have essentially treated it as if there is no current even present. But a similar argument is used in other situations without fault.  Take for example a conducting cylinder with a hollow, cylindrical shaped space inside. By the same argument there is no field inside.  To further illustrate my point, the derivation of the B field inside of a solenoid requires you to intercept the currents. You can’t simply do the loop inside of the air gap.  This, at least to me, seems like the same thing, and I can’t justify why one is incorrect and the other is incorrect. Please point out why I am stupid.
42447
What is the direction is the magnetic force vectors pointing from a coil of wire that has current running through it?    The above link is a picture of a wire with current running through it. I see the blue arrows indicating the magnetic field lines, but I am having trouble visualizing the magnetic force lines. Where are they pointing? Please help.
93233
Suppose that there is a semi-infinite wire which extends to infinity only in one direction. There are no other circuit elements at the other end(finite end) of the wire and the current does not loop. The magnetic field obviously has cylindrical symmetry when the Amperian contour is taken as a circle with its center on the wire.   However, due to charge accumulation there is a time-dependent electric field; hence a displacement current. How can I formulate the Ampere's law and show that the magnetic field is the half of that the infinite wire at the finite end of the wire? Do you think treating charge accumulation as a point charge with changing amount of charge right at the finite end of the wire will suffice?   The original question is:
24211
I'm currently studying from "Introduction to Electromagnetics" by D.J. Griffiths. In the book the significance of the displacement current term is explained by looking a non-steady capacitor circuit (shown below).  Using the integral equation and balloon-shaped surface, it is said that $I_{enc}=0$ but $\int \partial\vec{E}/\partial t \cdot d\vec{a}=I/\epsilon_0$. This statement makes sense to me - there is no physical current flowing between the plates but there is a changing electric flux through the balloon surface.  My misunderstanding is with the flat Amperian loop surface where it is mentioned that $\vec{E}=0$ and $I_{enc}=I$ in this case. Obviously there is a current flow $I_{enc}$ in the Amperian loop, but why is $\vec{E}=0$? Just looking at the equations directly, I would have thought there would be a combination of both current terms (including displacement current due to changing electric field in the wire) in a capacitor charging/discharging situation.  I've attempted to seek other explanations on this from other texts,  and elsewhere in this stackexchange site, but this has made me more confused. Clarification on this would be appreciated.     Differential form of Ampere's-Maxwell's equation: $$\nabla \times \vec{B}=\mu_0\vec{J}+\mu_0\epsilon_0\frac{\partial \vec{E}}{\partial t}$$  Integral form of Ampere's-Maxwell's equation: $$ \oint\vec{B}\cdot d\vec{l} = \mu_0I_{enc}+\mu_0\epsilon_0 \int \frac{\partial \vec{E}}{\partial t} \cdot d\vec{a} $$
48633
In electromagnetism books, such as Griffiths or the like, when they talk about the properties of conductors in case of electrostatics they say that the electric field inside a conductor is zero.  I have 2 questions:    We know that conductors (metallic) have free electrons which randomly moves in all directions, so how come we can talk about electrostatics which by definition means stationary charges? When the textbooks try to show why the electric field inside a conductor is zero they say let us put our conductor in an electric field. What happens then is that there will be an induced surface charge density which consequently induces an electric field within the conductor such that the total electric field within the conductor will be zero. That is perfectly understood, but my problem is the following: the original claim was that the electric field within a conductor is 0, not the electric field after putting the conductor in an external electric field it became zero. I do not understand the logic!
25007
I've got a few questions on induction and electromagnetic fields. My current understanding of induction and electromagnetic fields is that, when electricity/current flows through a wire, it creates an electromagnetic field. If you twist that wire into a coil then you can concentrate that field. You can then induce current into a different coil by placing it inside of the electromagnetic field created by the first coil.  So here are my questions:  Q1. Does the electromagnetic field contain any energy?  EDITED QUESTION  Q2. Electromagnetic fields are the same as waves, so does that mean that when current is induced, they get the energy from electromagnetic waves being exchanged, or do they induce current directly from the electromagnetic field?   Q3. If electromagnetic fields and waves are the same, then doesn't that mean that you can induce current from waves? Therefore transferring electricity over long distances?  Q4. What spectrum of light are the electromagnetic waves that are in a field created by electricity?  Q5. Finally, why is it not possible to induce current from the Earth's magnetic field? I thought Maxwell said that electric fields and magnetic fields were the same thing.   Thank you to anyone who answers.  Edited Q2: So my original question (although asked poorly) still stands. Where does the current that gets induced in the secondary coil come from? How does the electricity transfer from the primary coil to the secondary? For example, is it taken from the stored energy in the e.m field? Does the field just act as a bridge between the 2 coils? Or do the 2 coils exchange e.m waves which carry the electricity that is being transferred from coil 1 to coil 2? Or is it none of these things and something completely different?
44264
I am not sure which form of  is fundamental, integral form or differential form. Imagine an ideal infinitely long solenoid. When a current is changing in time, can we detect classical effects outside a solenoid, for example generating a circular current around solenoid by Faraday's law. If the differential form is fundamental, we won't get any current, but the integral form is fundamental we will get a current.
48139
A permanent magnet produces lines of magnet flux that we call a "magnetic field".  Those lines come from inside the magnet, come out of the N pole, loop outside the magnet, &amp; return back into the S pole to complete a magnetic circuit.  Using ferromagnetic materials, other magnets, &amp;/or test equipment, we feel &amp; measure forces that are caused by a magnet/s when other materials are placed within close enough proximity to the magnet/s (i.e. within their magnetic field/s).  We therefore conclude that the magnetic lines flow in a specific direction &amp; exert definite forces (i.e. magnitudes/strength) on some materials (ferromagnetic &amp; other magnets), depending on where those materials are placed within the magnetic field of a magnet/s.    We label those forces as "H Field" &amp; "B Field". We measure H in terms of Amperes/meter. We measure B in terms of Newtons/meter/Ampere (or Tesla). We also commonly defined B in terms of the force that it exerts on moving electric charges (i.e. the Lorentz force).  An "Ampere" is basic unit of electrical current in the SI system, which = 1 Coulomb per second--which is formally defined to be the constant current which if maintained in two straight parallel conductors of infinite length, of negligible circular cross section, and placed one meter apart in vacuum, would produce between these conductors a force equal to 2 × 10 −7 newton per meter of length.  A "Coulomb" is the standard unit of quantity of electricity in the SI system, which = the quantity of charge transferred across a conductor in which there is a constant current of 1 Ampere/Second.  Consequently, those "magnetic lines" are currents (or flows) of charges that don't appear to need any external source of energy to continue generating their currents.  We also know those magnetic lines exist inside a vacuum, so they are independent of air molecules to flow outside of a magnet.  So now my questions:   Exactly what charged particles are flowing outside (and inside) a permanent magnet that create the magnetic "lines"?   Do those particles come from something inside the magnet or does the magnet do something outside of it to affect unknown particles to make the lines? If there is a current (i.e. a continuous flow of charged particles), then why don't we harness that current like a water wheel (instead of 'using energy' to rapidly move copper wires through magnetic fields--like we do with electricity generators?)  Shouldn't we be able to get the line currents to charge a capacitor (or or other device) &amp; then otherwise discharge the capacitor for the energy that we want?
37648
Why is  due to external charge i.e a charge outside a closed surface equal to 0?  P.S:Moreover I found this statement confusing:-  Electric field appearing in the Gauss' law is the resultant electric field due to all the charges present inside as well as outside but the contribution of outside charges in producing flux is zero. Can someone help me understand it.
6330
My physics textbook says "Electrostatic field lines do not form closed loops. This is a consequence of the conservative nature of electric field." But I can't quite understand this. Can anyone elaborate?
99416
There are three ways of inducing current in a loop/coil of wire as shown in my book. We can have a magnet approach a coil of wire, or a wire approaching a magnet. Both can be understood in the same way.    On the other hand, we can also change the magnetic flux by pushing a loop of wire into a magnetic field.    This confuses me. Two vertical lines are cutting across the field. But since they are connected, the induced current, I conjecture, would cancel each other.  I saw in a YouTube video that to determine the direction in such situations as 2, one curl the fingers of their right hand along the wire, with the thumb pointing in the direction of the field. So the curled fingers are in the direction of the current. Basically the directions of current indicated by the thumb is always opposite the direction of the changing field.
62847
I want to find \$I\$, \$I_{D2}\$ and \$V\$ in this circuit. The diodes are made of Silicium. I'm a beginner and normally I would assume the Diode bias and then apply KVL to see if it is true. However, I've only encountered circuits where the wire forms a loop.    How am I supposed to apply KVL in this case? If voltage is the difference in potential between two points, how can I find the voltage of V if one point is outside of the circuit, therefore, outside of KVL application?
59540
There are several conditions that must be met in order for a force to be . One of them is that the curl of that force must be equal to zero? What is the physical intuition behind this? If you can, please explain it to me via the magnetic force fields because i have read that time-varying magnetic fields are not conservative because they do not meet that condition.I do not understand this.
58632
I would like to get some elementary intuition into the problem a solenoid fed with a time-dependent current, and the resulting current that such the solenoid field would induce in a loop completely outside the solenoid.  The classic situation is to imagine a perfect solenoid of $n_1$ turns per meter, having radius $a$ and fed by a current $I(t)=I_0e^{-t/\tau}$.  One places $N_2$ coils (all having radius $R&gt;a$) around the solenoid as illustrated by this picture from Haliday&amp;Resnick 10th Edition.      Using the usual Ampère's law argument shows the $\vec B$ field of the solenoid would be completely contained inside the solenoid, and homogenous across the cross section of the solenoid.    If there is a slowly varying current in the solenoid, will there be an induced current?  Presumably the answer is yes (at least according the HR solution manual): if we take the $\vec B$ field of the solenoid to be changing with time as a result of the current changing in time, but $\vec B$ still homogenous across its cross-section and $0$ outside, there is a change in the flux of this field through the surface bounded by the coils, and even though there is no magnetic field outside the solenoid where the coils are located.  The resulting change in flux induces an EMF independent of $R$, the radius of the coils, or for that matter the shape of the coil, provided it completely contains the solenoid.   If you are suspicious about the use of Ampère's law for slowly varying currents, the same solenoid field is obtained explicitly by Das Gupta in  "Magnetic field due to a solenoid." American Journal of Physics 52 (1984): 258-258, starting from Biot-Savart, which certainly holds for quasi-static currents.     But how can one intuitively grasp that no field outside the solenoid induces a current in a stack of coils located   completely outside this solenoid, in the region where $\vec B=0$?   A "classic" explanation might that the field might be $0$ but the vector potential is $\ne 0$, yet it seems this is invoking a lot of heavy machinery for a 1st year physics problem.  Moreover, Aharonov-Bohm-like explanations are really quantum in their nature and show that in quantum mechanics the potentials are the essential quantities.  Nota: a possible path of solution would be to invoke hidden momentum, along the argument .  Is there a simpler explanation?
37753
If the magnetic field doesn't polarize does it follow the electric field path of propagation? or does it vanish?
109325
When we have an uncharged conductor with a cavity and apply an external electric field, the charges rearrange to keep the electric field inside the metal zero. The driving force is the need to keep electric field inside the metallic layer, zero. Then why is the field inside the cavity also zero? I think this is because the charges would arrange in the same way as in the case of a cavity free conductor but why can't they arrange in a different way?  Why is this arrangement not possible which clearly has a field inside the cavity but not inside the metal?
21655
I'm trying to get my head wrapped around transformer operation and in the process regretting the times I snoozed in my Electromagnetics class as a EE student back when I was a lad :)  I'm looking for an intuitive understanding, but not just an analogous one. I'd like it to be grounded in the actual physics of what's happening. I've found several excellent sources on the web, but they all seem to skirt this question.  I've come across a few interesting hints and am now tantalizingly close, I think, but still yearning :)  Fact 1: Although varying sinusoidally, the "peak-to-peak" flux, so to speak, in a transformer's core is essentially constant (for a given voltage applied to the primary), regardless of the load.  My intuitive hypothesis was that variation in the "strength" of the flux was what transferred the energy from the primary to the secondary, but this fact would seem to contradict that theory. I had thought that the primary makes a bunch of flux based on the current flowing through it and the secondary sucks it up to make current of its own. No dice, it seems.  Then of course there's the fact that the formula for flux involves only voltage, time (frequency), and turns :)  Fact 2: The current in the primary is (approximately) 90 degrees out of phase with the voltage at no load, and approximately aligned in phase at full load.  This fact seems very promising and also curiously satisfying. It would imply that the Volt-Amps (VA) of the primary is constant and only the power factor changes as the current load on the secondary increases.  But I still don't get how the energy is actually being transferred. It seems vaguely like the flux is just there as an energy conductor or something and some other phenomenon is actually doing the energy transfer bit.  Can someone see what I'm missing and explain what's actually happening in there?