The magnetic field lines for a solenoid look like this:    As one can determine from the right-hand rule, the left side of the diagram contains the north pole and the right part the south pole. It makes sense to me that, near the north pole, the north pole of another magnet would move towards the solenoid's south pole. However, can somebody explain why the magnetic field lines inside the solenoid point towards the north pole? Does this mean if another magnet's north pole was placed inside, it would be attracted to the north pole of the solenoid?
120413
Is there any case where the direction of magnetic field inside a solenoid points from its North Pole to its south?
43824
In the B field of the loop, if R is the radius and z is the distance along the axis perpendicular to the center of the loop, let z go to zero, and multiply by N loops. Starting with the B field of the loop axis:  $$B=\frac{\mu_0 i R^2}{2(R^2+z^2)^{3/2}}$$ Becomes: $B_{\text{N loops}}=\frac{\mu_0 i N}{2R}$ and not $B_{\text {solenoid}}=\mu_0 i n$. What is the difference?
22284
I was watching Google map. Saw a line which is joinging north to south pole. It is going between middle of China and Mexico. But, the line is not straight. Tried to search in net but not able to get anything. Can anyone check and let me know  or
18076
So I came across this picture on facebook   My logic says it should show 200N, because you are pulling it with 100N on each side. On the other hand (as one of the facebook comments also stated, also saying is he is wrong he wasted 20k$ on physics degree), if you replace the right side with a wall you get this situation:    In this case I guess everyone agrees that the dynamometer would show 100N force. But if you isolate the dynamometer and "cut" the ropes on either picture, you would get the same thing. Because the system needs to be balanced, there would be 100N on each side.    And I study engineering too but I am confused by this. Why do we get the same distribution of forces, but dynamometer shows a different force?
115086
In my book, it is written that "An emf is induced in a loop when the number of magnetic field lines that pass through the loop is changing" (Faraday's law)  I understand that whenever there is a change in magnetic flux, there will an emf induced in a loop and this in turn will induce a current.  However, I really want to understand what exactly goes on to cause this. I just want to check if I am right:   There is a relative movement between the loop and the magnet (e.g. loop moving towards magnet) Thus, electrons in the loop are "moving" relative to the field A moving charge experiences a force perpendicular to the direction of the field As a force is exerted on the electrons, they move in a particular direction Current is induced   I do not know much calculus and studying high school physics but could someone please help me get an intuition behind Faraday's law or tell me if my way of thinking about it is right?
109036
I have a question about why this is true  $\oint B\cdot d\ell = \mu_0$ $I_{enclosed}$  My problem is that I am not really seeing visually or mathematically why the magnetic field generated by a current that doesn’t pass through the loop will not contribute to the integral.  Any advice or intuition is aprecciated thanks.
92998
How is the magnetic field at the centre of a loop of current or a solenoid effected by different cross sectional area?  I understand B=unI gives the magnetic field, but it does not specify how it changes as the area of the coil changes.  Thanks.
24909
In the textbook I'm reading it gives an example of where a person pulls a rectangular wire with a velocity $v$ and the left side of that wire is in a uniform magnetic field.    After some calculations, the author states that calculating the emf from the current induced in line $ab$ is equivalent to the work done by the person pulling the wire even though the force of the magnetic field has no effect on the work done by the person and the force exerted by the person has no effect on the emf. How is that the force produced by the magnetic field can produce an emf on line $ab$ if magnetic fields do no work?
69953
I want to ask about the workings of the . Why do the electrons come to rest on the edge of the wire? The magnetic field pushes them up, and the electric field pushes them forward. Shouldn't they reach the top of of the conductor and then stop moving up but continue moving forward?  Why does the magnetic field stop them from continuing to flow? The magnetic force is up so why would it effect their velocity forwards?
72792
I am sure there is a simple explanation for my confusion, but I am a little puzzled:  We are dealing with two parallel electron cannons that each produces a straight beam of electrons. They are placed at a distance d next to each other, which means there will be a repulsive electrostatic force between the electrons of the two beams. Also, according to the Maxwell equations, every moving electron will produce a magnetic field which then exerts another force on the other beam's moving electrons (similar to the effect that two currents in wires will cause an attractive force between the wires).   However, if we change the reference frame such that we are moving at the same speed alongside the electrons, there will be no magnetic field and no Lorentz Force. We are only left with the electrostatic force.  Do you guys know what might be the fallacy?
53701
I just took a rare earth magnet out of an old hard drive. Lacking an appropriate screwdriver, force was used, and the magnet broke into two pieces; one about a quarter of the original size and one about 3/4 the original size.  Let's say this is the magnet:  &gt;&gt;&gt;&gt;&gt;&gt;&gt;&gt;   and the arrows are pointing north, in the original magnet.  It broke into two pieces:  &gt;&gt;&gt;&gt;&gt;}   }&gt;   (where } represents the rough edge of the break).  I'd expect that the two magnets would keep their relative directions, so that the magnets would fit back together at the break, like this:  &gt;&gt;&gt;&gt;&gt;}}&gt;   But instead, the broken edges repel, and the magnet wants to come together so that formerly "north-facing" sides are now connected, like so:  &gt;&gt;&gt;&gt;&gt;}&lt;{   The obvious deduction here is that one of the pieces flipped polarities when the magnet was broken. I don't understand why this would be the case.  So why did one of the pieces flip polarities?  EDIT: To clarify, the actual magnet is a 120-degree arc of a circle. Thus, it's obvious what the original orientation of the pieces were. This isn't simply a case of me getting the pieces flipped over relative to each other.
89443
I don't know how this "paradox" can be solved. I'm given the following system: A permanent magnet with a magnetic field given by ($\hat{a}$ are unit vectors in the x and y directions)  $$\vec{H}=H_0\hat{a}_y$$  and a parallel plane capacitor with an electric field  $$\vec{E}=E_0\hat{a}_x$$  Poynting's vector is given by:  $$\vec{S}=\vec{E}\times\vec{H}=H_0E_0\hat{a}_z \neq 0$$  The funny part comes when the professor told that in a system like that "clearly" there is not propagation (wich I know will imply some short of energy flux) in the $z$ direction, hence the "paradox". Is there or is there not propagation of energy?  Any hint will be appreciated, thank you for your time.
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.
59789
I've been stuck on this problem for about an hour.     In an ideal transformer, the same flux passes through all turns of the primary and of the secondary . Show that in this case $M^2=L_1L_2$, where $M$ is the mutual inductance of the coils, and $L_1$, $L_2$ are their individual self-inductances.   My first instinct was the following: If we isolate the response of each coil to the other one, we get the equations $N_1\Phi_1=MI_2$ and $N_2\Phi_2=MI_1$, where $\Phi$ is magnetic flux going through a single turn of the coil and $I$ is current. Likewise, if we isolate the response of each coil to itself, we get the equations $N_1\Phi_1=L_1I_1$ and $N_2\Phi_2=L_2I_2$. I would now naturally want to say "Now just multiply $N_1\Phi_1$ and $N_2\Phi_2$ both ways, and get the desired result!" i.e.,  $$(N_1\Phi_1)(N_2\Phi_2)=(MI_2)(MI_1)=(L_1I_1)(L_2I_2)\implies M^2=L_1L_2$$  But that's incorrect, because the response of the coils to themselves and to the other coil are different quantities (i.e. not necessarily equal).  Realizing this, I write down the more general equations.  $$N_1\Phi_1=MI_2+L_1I_1$$ $$N_2\Phi_2=MI_1+L_2I_2$$  Now even with the hypothesis that $\Phi_1=\Phi_2=\Phi$, I still can't see how the identity $M^2=L_1L_2$ follows. Could you help clear up my confusion?  *Taken from D. Griffiths Introduction to Electrodynamics (4th ed.), Problem 7.58.
81840
A metal rod of length $l$ is placed (as shown in figure) in a cylindrical time varying magnetic field. Find the potential difference across it.   My answer:  As electric fields as forming circles around the centre with magnitude $$\frac12r\frac{dB}{dt}$$ whose magnitude is same along any chord at a fix distance from centre: $$\Delta V=E.l=\frac12r\frac32at^{\frac12}.l$$ $$\Delta V=\frac34arlt^{\frac12}$$  My question: Is $\Delta V =V_M-V_N$ or $\Delta V=V_N-V_M$ $\bf OR$ equivalently which side is at high potential?  Possible    $(i)$ As Field lines are circular from $M$ to $N$, $M$ must be high potential. $(ii)$ As this field line apply a force on electrons- in the rod- towards left, then $M$ must have excess $e^-$ and $N$ must have deficiency; so $N$ would be high potential as $M$ is $(+)$ and $N$ is $(-)$.
11443
Why does a moving (at constant velocity) magnet release more energy in the form of magnetic fields when the number of charges placed near it are increased? Say two current carrying coils $C1$ and $C2$ are in a system in which $C1$ is moving at constant velocity. The magnet fields from $C1$ will reach $C2$ after an interval of time. So at the moment $C1$ releases energy (M.F) it doesn't know about charges surrounding and it can't make predictions of how much energy is to be released at the instant. So it can only give out a fixed amount of energy in M.F.  Let's say it is equal to $M'$. When we add another coil say $C3$ in system, the amount of energy released by C1 is still $M'$. Therefore the total output can't exceed $M'$.  This statement says that you can't get more wireless energy by constant velocity gaining magnet in output even if you use many sets of coils.  But I think that it is false and we can get larger amount of energy as output by using extra coils. C2, C3, ... Cn Explain what is right
81267
When you hold a powerful magnet near an old-style CRT TV, you see an interesting pattern, which "shows up the field lines" (see  ).   I understand the basics about the general idea why the image is distorted due to electron deflection, as described in , but am curious as to why the specific pattern of alternating light and dark regions is seen. Do the electrons follow certain field lines preferentially, leaving other regions of the phosphor screen dark?