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All the other answers that say the "single" integral is simply a shorthand notation are right, but it is well to remember that one can indeed construe the integral as a single integral as a Lebesgue integral (if you do nothing else, look up Lebesgue's very cute little half paragraph summary (on the Wiki page) of his idea in a letter to Paul Montel). If ...

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It is, in fact, a double integral! The first notation used $$\varPhi_E = \oint_S \vec{E} \cdot \mathrm{d}\vec{A} = \oint_S \vec{E} \cdot \hat{n} \ \mathrm{d}A$$ is simply a more compact notation. It's much easier to write $\mathrm{d} \vec{A}$ instead of, say, $r \ \mathrm{d}r \ \mathrm{d}\theta$ all the time. Furthermore, it's more general, as $\mathrm{d} ... 3 The general formula is indeed a double integral, so the most technically correct way to write it is $$\Phi_E = \iint_S \vec{E}\cdot\mathrm{d}^2\vec{A}$$ But when formulas start to involve four, five, or more integrals, it gets tedious to write them all out all the time, so there's a notational convention in which a multiple integration can be designated by ... 5 It is just a more compact notation. It is implied by the integration element$dA$that you are integrating over the surface. 2 Yes , that's easy because mAh is presented for a specific voltage that battery can output. Because the battery must output at a specified voltage. Your 5600mAh is for 5 volts. If it's not 5 volts. You must recalculate it. But the voltage shouldn't be change if the battery is not adjustable. Hope you understand 2 John Rennie's answer is correct for a DC series connected motor and, almost certainly, this is the kind of motor you (the OP) are talking about. An interesting way of writing John's answer "backwards" is that you have just observed the reason why the most powerful traction motors are exactly this kind of motor - almost all DC train and tram motors are ... 2 The pairs of lines are the same phase and at the same voltage - they are really just a single thick wire split into two thinner ones. It is easier to install two smaller wires to double the current capacity than a single thicker wire. It is easier to handle the lighter cable and you can stock just a single gauge of wire and handling equipment. It also ... 2 Three-phase has two main reasons to exist: Driving N. Tesla's polyphase induction motors used throughout industry. Reducing the total cost of metal in cross-country power lines: w/single-phase lines, more metal would be needed to transfer the same rate of kilowatts. You're right: lighting as well as AC motors will briefly turn off at 120 times per second ... 3 Think of it in terms of current, V, W, and Z are in series, so each is equally bright. X and Y are in parallel, so each gets half the current of the others. If you assume each bulb is a constant resistance R (not true for incandescent bulbs, by the way), then V,W and Z will each dissipate$i^2R$. For X and Y, since each has a current i/2, the power will be ... 2 When a motor is turning it acts as a generator and produces a back EMF that opposes the applied EMF. See my answer to Top angular speed of electric motor for more on this. A frictionless motor would draw no current when not under load, though obviously real motors do draw some current because of frictional losses. If you load the motor you reduce the back ... 0 The resistivity of a given substance (air) is fixed. For constant potential difference, current will change as$I=\frac V R$. However, air is not an ohmic substance so ohm's law does not apply for air. 0 Current is produced in a metal when the free electrons in the metals acquire a drift velocity due to an electric field. But when these free electrons travel through the metal, their path is hindered by other atoms and particles and their electomagnetic pull. More the resistance, higher is this hindrance and lesser is the drift velocity. Hence, the current ... 1 The answer depends on the circumstances: how do you change the resistance? Both the drift velocity and the number of available charge carriers can be changed. In a basic Drude model for electrical transport both,$n$, the charge carrier density and$\tau$, the time between collisions determine the resistance: $$\mathbf{J} = \left( \frac{n q^2 \tau}{m} ... 1 Your understanding is correct. From V=IR if voltage stays the same while resistance is increased, the current should be decreased. But if you have heard of another equation I = \frac{Q}{t} If current(I) is increased and the charge Q is fixed (Charge is fixed if the power supply is from power cells like battery). Time will be decreased. Which means ... 1 The whole (pedagogical) point of the slide wire generator is to illustrate that not only do changes in the magnetic field generate current in the loop, changes in the area of the loop - in a constant magnetic field - also generate a current. It's the change in magnetic flux that matters. As long as the wire is moving with some velocity, the magnetic flux ... 0 Let the battery voltage be V_S. Then, the battery current is$$I_S = \frac{V_S}{(100 + 100||100)\Omega} = \frac{V_S}{150 \Omega} $$The current through the series (left-most) resistor is just I_S and the current through each parallel resistor is just I_S/2. Since the resistor power is given by$$p_R = R \cdot I^2_R$$the power delivered to the ... 0 There are two kinds of "earth" being talked about here. There is: The kind that aims to use the ground itself as a "return path"; and A protective "earth", which is actually a separate conducting line laid throughout a building. For the "return path" earth of 1. there are several ways wherein this will work: There is actual conduction (i.e. drift of ... 0 Actually according to my opinion it give you a shock but it is negligible. If you give a high energy and try to make contact with earth it will neutralize by giving a little to you. The reason is, if there is a good conductor like body it goes through the body other than only earth. Just take a lightning application and think of that. 3 Earthing something means dumping the electron flow into the earth. Since the earth is so big, it can absorbe/give a practically infinite amount of charge without changing potential, this means that you can treat earth as a reservoir of ready to use electrons. If you plug the phase of your home power line into the ground (without safety devices in the ... 3 The switch really has 2 positions: on and off. However, when you move the switch very slowly, it may leave the closed position slowly. When the switch is just barely open, the field may cause the air to break down and start conducting, to form a spark (as @anna v explained). To rephrase, the reason why sparks happen is because the switch may only be open a ... 2 Air is a bad conductor up to a certain value of the field generated by charges and the distance between them. After that air breaks down and a discharge happens, i.e. sparks. So below this level charges can accumulate by rubbing for example , positive ions left on one surface and negative on the other. When brought close a spark occurs. Why does holding ... 0 It depends on what exactly you mean by electricity. When you're thinking about electricity moving this could be an electric current, or it could be an electric field. The obvious example of the first is current flowing in a wire, and the obvious example of the second is a radio wave travelling (at the speed of light) between the transmitter and your radio. ... 0 Faraday's law is given as follows$$\oint \vec{E}\cdot\vec{dl} = -\frac{\mathrm{d} }{\mathrm{d} t}\iint_{ }^{ }\vec{B}\cdot\vec{dA}$$Look at the R.H.S of the equation. It is the changing magnetic flux( w.r.t time ) that is responsible for the induced E.M.F. Although the coil of the solenoid does not consist of perfect conducting loops, the magnetic flux ... 0 Basically, when an electrification takes place, electrons are not created but they are transferred..... in the case of comb attracting tiny tiny bits of papers when rubbed with dry hair is because electrons from the dry hair gets transferred to the comb and now the comb induces a dipole in the bitties of paper and the paper gets attracted... 1 I found out that they mention about whole ions being moved in the human nervous system in order to transfer an electric impulse Electric impulse I think u mean signal. Take look on Action potential there picture demonstrates moving of signal. So neural signals are not current itself, or moving ions from head of neuron to his tail(transferring ... 1 magnetic flux linkage is negative A good observation. Now, the magnetic flux associated with a surface is given by \iint{ }{ }\vec{B}\cdot\hat{n}\mathrm{d}A The surface could be an open one or a closed one. Let us consider an open surface as shown below For an open surface, the area vector could be in any direction ( I've chosen an arbitrary ... 1 The key to electricity is that it is moving charge. In our electrical wires we use electrons, which carry charge, to send signals. The current is the net flow of charge through a wire (or whatever is carrying the current) which then depends on the speed. The speeds at which electrons move involve a few distinctions. Firstly, the electrons move randomly due ... 1 Magnetic flux is a scalar quantity and its positive/negative sign indicates the direction of the magnetic field. And the Faraday's law of induction is a quantitative version of Lenz's law, which may help your understanding: \oint_{\partial \Sigma} \mathbf{E} \cdot \mathrm{d}\boldsymbol{\ell} = - \frac{d}{dt} \iint_{\Sigma} \mathbf{B} \cdot ... 2 Yes, magnetic flux can be negative. It just depends on where the field is going. Say there is a sheet and magnetic field is going through it from front to the back, we can call the flux there as positive and negative when it's the other way round. It is pretty clear from the statement of Lenz's Law why the emf defined is taken as negative: An induced ... 1 The work required to move a charge q between two locations a and b with a voltage difference V_{ab} is$$w=V_{ab}q.$$Differentiating with respect to q, one obtains$$\frac{dw}{dq}=V_{ab},$$which is how the book got the equation. Basically, the intuition is that voltage is "work per charge moved". 0 it doesn't seem to have anything to do with phasors But it does since this is the way one adds phasors. Assume you have two series connected circuit elements with phasor voltages that differ in phase by the angle \phi.$$\vec V_1 = V_1\vec V_2 = V_2e^{j\phi}$$Since the voltage across the series combination is the sum of the individual phasor ... 1 V_L and V_R are phasors which are 90 degree out of phase. Like two vectors, phasors follow the same rule for addition that's why they have used pythagoras theorem. 0 You'd be lucky to even generate 1 Watt. Compare yours to this much larger 10 Watt generator intended to operate off hundreds of degrees of temperature difference: http://www.devilwatt.com/products/17-10-watt-camping-stove-thermoelectric-generator 0 The details of how your particular device will perform is very much a function of how that device was constructed and how it will be used, but in general, the physical effect is called the Seebeck effect -- briefly, the conversion of a temperature difference across a device to a voltage. Efficiency for such devices is actually quite low, with \eta = 0.02 ... 0 try taking a look at this page it goes in to good detail about inductors in a dc circuit. http://www.ibiblio.org/kuphaldt/electricCircuits/DC/DC_15.html 4 Thare is only one node connecting elements B, D, E, and G. The dots on the diagram are just to indicate that the lines do in fact connect, so that all of the wires are part of the same node. In this kind of schematic diagram wires are considered as ideal, and all points on the wire are considered to be at an equal potential. 0 I thought static electricity doesn't really build up when there's a lot of moisture, so that's why you don't get static shocks in the summer when there's more humidity. Even though it's winter now, I figured I wouldn't feel any static shocks if my hands are wet, but I still do. When the air contains more moisture, electron build-up on your body and ... 0 If you're looking to produce power from a temperature differential, go with a device optimized for the Seebeck effect. Peltier and Seebeck effects are essentially the same thing, or rather flip sides of the same thing, but thermoelectric generators (Seebeck) are optimized differently from thermoelectric coolers (Peltier). 0 For 1, you are spot on. The output voltage and current are multiplied to get the power. Numbers in the press are often optimistic. It may be a peak power, rather than one that can be sustained if they were willing to release enough water over a long period. 1 Hot water is more conductive than cold water. 1 I see you edited the question from a sauna to what I assume is a insulated test chamber. Steam would have very little change in the voltage required to getting a spark. You would also need more than just a bare wire, you would need a grounding plate inside your chamber. The voltage would primarily be a function of the air gap separating your wire and your ... 2 The electrical conductivity of the water depends on the water temperature : the higher the temperature, the higher the electrical conductivity would be. The electrical conductivity of water increases by 2-3% for an increase of 1 degree Celsius of water temperature. Many EC meters nowadays automatically standardize the readings to 25oC. While the electrical ... 2 Yes, it is possible. The simplest qualitative answer to this is that, at the microscopic level, the electrons in a conductor are dictated by quantum mechanics, which is inherently probabilistic. Velocities and positions are rarely ever totally excluded from a given value; it's just insanely unlikely for a single electron to attain that given value. ... 1 While DumpsterDoofus is right, perhaps this explanation might be helpful. A dipole is an asymmetric separation of charge, like this: + -. A dipole can have many charges. The total charge must be 0. The center of charge for the + charges and the center of charge for the - charges must be at different places. A dipole can exert electrical forces on ... 0 So, why molecules with mirror symmetry have no permanent dipole moment? That's actually not true. For example, hydrogen cyanide has an infinite number of mirror planes of symmetry, but has a nonzero permanent dipole moment. Also, formaldehyde has two mirror planes of symmetry, and a permanent electrical dipole moment. However, for any molecule with ... 0 If a molecule has mirror symmetry then charge distribution will be uniform. Charge distribution on the left of the molecule will be equal to the charge distribution on the right effectively cancelling out, resulting in no permanent dipole moment. On the other hand if a molecule has no mirror symmetry then there will be a direction where charge distribution ... 0 Your reasoning is correct. If the solar cell is modelled as a voltage source E in series with an internal resistance r and the cell is connected to a load resistance R_L, the series current is given by Ohm's law:$$I = \frac{E}{r + R_L}$$or$$E = (r + R_L)\cdot I$$The output voltage$V$of the solar cell is the voltage across the load ... 0 Electrical current can be carried by conduction electrons, or by 'holes'. For ordinary matter, there is roughly one electron per two daltons of matter, which is to say,$\frac 12 N_Ae$. This roughly works out at$480*10^6\$ coulombs per kilogram. Many of these electrons are bound in the inner orbitals, but there are still plenty of conduction electrons ...

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but when they are pushed in the same direction, they create what we call an uniform electric field Movement of electrons in the same direction does not create a uniform electric field. Two infinite parallel plates with an electric potential difference between them, and no movement of electrons or other charged particles, would set up a uniform ...

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The electron cloud is not exacly centered at the proton in the hydrogen atom (or about the nucleus in other atoms). This is analogous to the Moon not exactly orbiting about the Earth, but the Earth and the Moon each orbiting about their barycenter (center of mass of the Earth - Moon System). In solving the Schrodinger equation for the hydrogen atom, it ...

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