# What is Induced emf: Definition and 251 Discussions

In electromagnetism and electronics, electromotive force (emf, denoted

E

{\displaystyle {\mathcal {E}}}
and measured in volts) is the electrical action produced by a non-electrical source. Devices (known as transducers) provide an emf by converting other forms of energy into electrical energy, such as batteries (which convert chemical energy) or generators (which convert mechanical energy). Sometimes an analogy to water pressure is used to describe electromotive force. (The word "force" in this case is not used to mean forces of interaction between bodies).
In electromagnetic induction, emf can be defined around a closed loop of conductor as the electromagnetic work that would be done on an electric charge (an electron in this instance) if it travels once around the loop. For a time-varying magnetic flux linking a loop, the electric potential's scalar field is not defined due to a circulating electric vector field, but an emf nevertheless does work that can be measured as a virtual electric potential around the loop.In the case of a two-terminal device (such as an electrochemical cell) which is modeled as a Thévenin's equivalent circuit, the equivalent emf can be measured as the open-circuit potential difference, or voltage, between the two terminals. This potential difference can drive an electric current if an external circuit is attached to the terminals, in which case the device becomes the voltage source of that circuit.

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1. ### Maximum voltage in the primary circuit of a transformer

The alternating current will create an induced voltage given by ##V=-N\frac{d\phi(\vec{B})}{dt}=-N\frac{\Delta\phi(\vec{B})}{\Delta t}=N\frac{2 B_0 S}{\Delta t}=\frac{240\cdot 2\cdot 65\cdot 10^{-3}\cdot 10\cdot 10^{-4}}{10\cdot 10^{-3}}=3.12 V## and since this is the effective voltage, the...
2. ### How Can I Simulate Induced EMF in a Coil Using Ansys Maxwell?

Hi guys, I'm new to this forum. I'd like to know how I could perform a simulation to find the induced EMF in a coil placed closer to a current-carrying conductor. I'm not sure how I should model the coil. I tried modelling it as a solenoid but the solenoid exceeds my required length when I enter...
3. ### I Questions about cancelation of induced EMF and minimizing eddy currents

I recalled a drawing that was provided in an EM text. Without going in length, the basics is simple - in order to minimize eddy currents one divides up a planar surface area of a wide conductor into small separate sections. As is done in transformer core laminations for example. In the image a...
4. ### Calculate the induced EMF of a rotating loop

there are a bunch of problems in this section that ask similar questions, but they ask the amplitude and this doesn't. this is an even problem so i do not have the answer, but my hunch is that it is not an amplitude question. i solved for the amplitude so i am guessing i got this one wrong...
5. ### Induced EMF due to motion of a wire perpendicular to a magnetic field

This question appeared in a university entrance exam.Basically, if magnetic flux passing through a surface of a loop changes over time ,only then e.m.f will be induced to that loop.But here only a straight line is used and there's no chance of forming any area.So by definition there's no chance...
6. ### Using Faraday's laws to find the induced EMF

Here is the question: We know the equation \epsilon = \frac{d\phi }{dt} = BAcos(\theta ). This means that the only way we can create an induced voltage is if we change the magnetic field, change the area of the loop in the magnetic field, or change the angle between the normal vector to the...
7. ### Drop height of a magnet vs. induced EMF in a solenoid

I am currently working on an experiment that involves dropping a magnet from varying heights and measuring how the induced emf of a solenoid changes as a result. I am currently somewhat struggling with a derivation for a relationship between the two variables, however, this is what I have been...

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9. ### I Unveiling the Proof of Induced EMF Formula: E = ∫ (v x B) · dl

Why is ##E = \int (\vec v \times \vec B) \cdot d \vec l##? This seems to be a general formula, and I would like to know its proof. Thanks for all the help.
10. ### Induced EMF in a small square loop of wire at center of an AC Circuit

I used the voltage of the power supply and resistance to solve for the current in the larger circuit (20V/5ohms=4 amps). I am not sure if the equation listed above is the correct one I should be using, but I tried it using the following numbers. For omega, I used 2*pi*frequency. N should...
11. ### What is the magnitude of the induced EMF?

I did the question in this way as attached. I got the crrect answer, but I feel unsure if it is the right way of doing it.
12. ### B What Is the Correct Calculation for Induced EMF in This Circuit Scenario?

I think the answer to the first question is 3V and the answer to the second question is 6V Does anyone have a different answer?

14. ### DC generator: Induced EMF of a single coil armature

Hi. I am reading a textbook about simple DC generator. The situation is if we are rotating a single armature coil within a constant field B, the induced emf will be (if we are to only think about the magnitude), emf= B*l*W*omegaB = magnetic field l = length of the coil W = width of the coil...
15. ### Induced EMF in a moving Loop Conductor

I am having trouble figuring out if the circular loop has an induced current. One explanation is ∫ E ds = -d Φ / dt. Since flux = B ⋅ A, a change in the magnetic field would require a change in the magnetic field, a change in the area, or change in direction of either vector. Since none of...
16. ### Induced EMF and current for a bar sliding on a circular rail

On the left: my copy of the illustration in the problem. On the right: top view, with the angle. The problem gives the magnitude of the magnetic field, the radius of the rail, the resistance of the resistor, the initial rotational frequency of the bar. I am able to obtain the given solutions...
17. ### Solving Faraday's Law: 0.73V Induced EMF Help Needed

I have a simple sketch of the diagram, and I know I must use the vertical component of the magnetic field of the Earth when doing this problem I got an induced emf of 0.73 volts but I do not know if I correctly substituted the right values into faraday's law equation? Any help will be really...
18. ### How to find the charge at time = t (at any instant)

I was not able to derive the charge on the capacitor. But then, I arbitrarily assumed ##\phi=B.A## (Dot product of Magnetic field and Area) Then, proceeding as follows, ##\phi=BA\cos(\omega_0 t)## ##\frac{d\phi}{dt}=−BA\omega_0\sin(\omega_0 t)## Now at ##t=0, \phi=BA\cos(0)=BA## Therefore...
19. ### The Magnitude of Induced EMF in a Moving Rod?

Homework Statement: A 25.0 cm long metal rod lies in the xy-plane and makes an angle of 36.9 with the positive x-axis and an angle of 53.1 with the positive y-axis. the rod is moving in the +x-direction with a speed of 6.80 m/s. the rod is in a uniform magnetic field B=...
20. ### EMF induced in a rotating rod having mass

I first calculated induced emf and then calculated torque about O.But what will i do further.I think i need to find current and then fidn emf=IR. Help please.
21. ### Calculate Induced EMF in Circular Loop: Cylindrical Coordinates

In order to calculate for the curl of the induced electric field for a loop moving in a uniform magnetic field, and using the cylindrical coordinate system for a curl, it's my understanding that since the B field is in the 𝑧̂ direction, then so is the partial time derivative of B, and therefore...
22. ### Finding the induced EMF in a solenoid-wire system

I know that ##B = \mu n I## and ##\phi = B \pi R^2##. So with have ##d\phi / dt = \mu n \alpha \pi R^2##. But I don't know what to do with this? is this the answer? I don't think so but I don't know what to do after this.
23. ### Need someone to check my equations and work on this induced EMF problem

a magnetic field has a magnitude at time t of 4.5x10^-5 T +(2.6x10^-6 T/sec)t. the field points in the positive z-direction. a rectangular wire loop, which is 0.3 meters by 0.4 meters, lies in the xy-plane. Note: If the z axis points out of the paper. a.) What is the induced emf in the loop...
24. ### Exploring EMF and Faraday's Law in LR Circuits

1) Take a non-steady circuit such as an LR circuit. Why does Kirchoff's voltage law work when analyzing such a circuit? Is it because we're assuming that dI/dt and thus dB/dt are approximately zero thus meaning that curl E is approximately zero? 2) ε, the electromotive force, is the line...
25. ### Current induced on a coil by a changing magnetic flux in another coil

I will first calculate the magnetic flux of the coil in motion. $$\frac {d\phi}{dt} = -\frac {dB_{loop}}{dt}A = -\frac{d}{dt}(\frac{\mu_o}{4\pi}\frac {2\pi NR^2I}{(R^2+z^2)^{\frac{3}{2}}})A$$differentiating in terms of ##z##, we get \frac {d\phi}{dt} =(\frac{\mu_o}{4\pi}\frac {6\pi^2...
26. ### Induced EMF — generator coil area calculation

Homework Statement What is the necessary area for a generator that produces an emf of ##\mathcal{E} = 150V## when it spins at a ratio of 60 revolutions per second, in a magnetic field of ##B = 0.5 T##? Homework Equations ##\oint_{c} E \cdot dl = \mathcal{E} = -\frac{d}{dt}\iint_{s} B \cdot dS...
27. ### Induced EMF in closed loops around bar magnet

I wonder if there is a way to calculate induced EMF in closed loops around bar magnet, which is traveling with constant velocity v to the right as depicted?
28. ### What is the amplitude of induced EMF in a magnetic dipole antenna?

1. A magnetic dipole antenna is used to detect an electromagnetic wave. The antenna is a coil of 50 turns with radius 5.0 cm. The EM wave has frequency 870 kHz, electric field amplitude 0.50 V/m, and magnetic field amplitude 1.7 X 10-9 T. (b) Assuming it is aligned correctly, what is the...
29. ### B How do you calculate induced EMF in an open loop with changing magnetic field?

Let's say you have an open loop (like a section of a circle) in a changing magnetic field. I think there would be an induced EMF, but no current. What I can't figure out, though, is how to calculate the induced EMF. Using Faraday's law doesn't seem to help, as there's no enclosed area.
30. ### Calculate the induced EMF for angle α

I have a question in my book and it’s confusing me a bit. I tried to search online for similar solved problems but couldn’t succeed. So here it goes:Calculate the induced EMF in a conductor loop when the angle between \vec{A} ~ and~ \vec{B} ~is~ changed ~from ~{0 °}~ to ~{α °} in 1 second...
31. ### Induced EMF and current in the circuit

Homework Statement Homework EquationsThe Attempt at a Solution First I will label a few points . A is the point on the ring touching the rails , vertically below P . B is the point on the ring touching the rails , vertically below Q . T is the topmost point on the ring . M is the bottommost...
32. ### What equation for induced EMF?

I understand the direction compnent of this question. But I don't understand where the magnitude of the induced current came from? I'm assuming faradays law wasn't used as there wasn't a change in magnetic field?
33. ### Find the maximum amplitude of the induced EMF

Homework Statement [/B] A radio transmitter radiates isotropically at the frequency of 90.8 MHz. The peak magnetic field at a receiver, 9km from the transmitter, is ##9x10^{-10}T##. Calculate the maximum amplitude of the induced emf in a 12 turn coil with area A = ##90cm^{2}## at the receiver...
34. ### How Accurately Can Induced EMF Represent Batteries in Circuit Problems?

Homework Statement Homework EquationsThe Attempt at a Solution Sorry for the unclear image . EMF induced in the left loop = 8 Total Resistance of the left loop = 6 Ohms Current will be induced in anticlockwise direction in the left loop of magnitude 4/3A. EMF induced in the right...
35. ### Inducing EMF Through a Coil: Understanding Flux

Thank you for reading my post. I can understand why a change in magnetic flux through a conducting surface would induce an emf, but how does this work when inducing an emf through a coil? How does the flux through the empty space between the wires have an effect on the electrons in the wire...
36. ### Flux in a Uniform Magnetic Field

Thank you for reading my post. I was thinking about induced emf and magnetic flux and I realized I have a huge misunderstanding, but I don't know exactly what it is. Below I will list 4 statements which I logically know cannot all be simultaneously true. Can you please tell me which one(s) are...
37. ### Current flowing in a cylinder and induced EMF

Homework Statement Homework EquationsThe Attempt at a Solution The current will decrease , as a result an EMF will be induced in the cylinder . The EMF induced E = -dΦ/dt I am assuming magnetic field through the cylinder to be same as that at the center of the a current carrying coil...
38. ### Induced EMF in a coil outside a solenoid

Homework Statement [/B] A conducting coil of radius R is outside a long solenoid with a cross section of radius r. What is the emf induced in the coil? Most example problems of this type I think are solved based on Faraday’s Law. These examples do not use the distance from the solenoid to the...
39. ### B What's the relationship between drop height and induced emf?

In my experiment, I intended to find out how the change in the bar magnet drop height from solenoid affected the emf induced in the solenoid, however, I am unable to come up with an equation that shows a relationship between the two variables. I have thought of Biot-Savart law, but I do not...
40. A

### Induced EMF between two points

Homework Statement Homework EquationsThe Attempt at a Solution First part is easy . Area of the triangular loop is A = (1/2)(2R)(R) = R2 Induced EMF in loop ABC = Rate of change of flux = dΦ/dt = AdB/dt = R2(dB/dt) which is correct . Now the second part has stumped me . I would really...
41. R

### Fairly hard induced EMF problem

Homework Statement (ignore the suggested problems for test 3.) If for whatever reason the image doesn't load the given's are that: The area is 25pi(.125m)^2 (A circular coil with 25 turns and a radius of 12.5cm.) The magnetic field varies with time and is...
42. ### Induced Voltage of Rotating Circular Loop

HI! I'm a student, this question appeared in one of the old tests. I though I had it solved but apparently I must have missed somewhere. Could someone please at least hint me where I went wrong? Homework Statement Thin wire is wound into circular frame with radius ## r = 0.05m ## which...
43. ### I Induced EMF in a half vs. whole ferrite toroid

Hello all - I've stumbled upon what seems to be a pretty basic magnetic materials question that's got me stumped. Maybe one of you can help me figure this out. I did the following experiment (see figure below): Put a ferrite toroid around a current carrying wire carrying 12 Amps RMS at 120V...
44. ### Induced EMF graph of a very small wire moving through a coil

Homework Statement Homework Equations induced emf = - d(magnetic flux)/dt The Attempt at a Solution [/B] I believe the graph will start initially curving upwards, because it begins to cut more and more flux lines which lead to an increased induced emf. Once it is "fully" within the...
45. ### Flux and Induced EMF vs displacement graphs

Homework Statement A small coil of wire is situated in a non-uniform magnetic field. The coil consists of 40 turns of wire and moves with a constant speed in a straight line. The coil has displacement x from a fixed point P. The variation with x of the magnetic flux in the coil is shown in the...
46. ### The induced EMF in an inductor

Homework Statement A generator consists of 500 turns each of surface area 7/11 m² . It rotates at rate of 50 revolutions per second (f =50 Hz), in a field of magnetic flux density of 5*10^-4 T, its terminals were connected in series with a capacitor (Xc=110Ω), an inductor (Xl=80Ω) and a...
47. ### Flux through rim created by moving circuit and induced EMF

In Purcell- Electricty and Magnetism book, in the chapter on electromagnetic induction, I found the following explanation regarding the magnetic flux through a circuit of area ##S##. Consider the circuit in figure, moving in a time ##dt## in a magnetic field ##B##, constant in time (but not...
48. ### Drawing flux and induced EMF graphs - Faraday's/Lenz's law

I would really appreciate some clarification about how to draw graphs showing changing flux and induced EMF. I understand that there needs to be a 90 degree phase difference as the EMF is a maximum when the flux has the greatest rate of change. However, our exam board says that the EMF can be...
49. ### B The factors determining the induced EMF in a wire

The induced emf in a straight wire is determined by the equation (emf=Blv sinθ) where θ is the angle between the direction of the motion and the lines of the magnetic field, and frequently, I see diagrams like these explaining the phenomenon: In those pictures the wire is perpendicular to the...
50. ### Induced EMF in a circle: Faraday's law

Homework Statement Explain what happens in the following situation: You have a loop in the form of a circle and there is a varying magnetic field inside that loop as the following picture illustrates: Homework Equations Faraday's law lorentez force The Attempt at a Solution I first thought...