# Drawing flux and induced EMF graphs - Faraday's/Lenz's law

• Amanda H
In summary, the conversation discusses the confusion around drawing graphs for changing flux and induced EMF. The questioner understands that there needs to be a 90 degree phase difference between the two, but the exam board states that the EMF can lead or lag by 90 degrees. The expert clarifies that the negative sign in the Lenz's law indicates that the induced EMF opposes the change in flux and this can result in either a leading or lagging EMF. They also mention the dot convention in inductors, which determines the direction of induced EMF based on the winding direction. The expert suggests that when drawing the graph of EMF, the sign of dΦ/dt should be opposite to the sign of induced EM
Amanda H
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 either leading or lagging by 90 degrees. I don't understand this as surely the as the the EMF = negative gradient of flux then the EMF must be negative when the flux is a positive gradient and vice versa. Please help. This is driving me mad!

Amanda H said:
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 either leading or lagging by 90 degrees. I don't understand this as surely the as the the EMF = negative gradient of flux then the EMF must be negative when the flux is a positive gradient and vice versa. Please help. This is driving me mad!
I believe the negative sign in the Lenz's law says that the induced emf "opposes" its cause i.e. change in flux. This means the emf is induced in such a way that the resulting current would try to make up for the change in the original flux.

Look up dot convention in inductors (or transformers). Direction of emf induced between two ends of a coil depends on the sense of the winding.

Thank you for helping out. So, what you are saying is that the negative sign in the equation can be ignored when drawing graphs and that the Emf can either lead or lag as this is simply due to the winding...?? This is what I thought but if you see the following link the explanation of the Emf graph describes a positive and negative gradient of the flux...
https://www.google.co.uk/search?q=c...&q=flux+and+induced+emf&imgrc=rd3_kOmysfILDM:

Amanda H said:
Thank you for helping out. So, what you are saying is that the negative sign in the equation can be ignored when drawing graphs and that the Emf can either lead or lag as this is simply due to the winding...?? This is what I thought but if you see the following link the explanation of the Emf graph describes a positive and negative gradient of the flux...
https://www.google.co.uk/search?q=current+and+induced+emf+graphs&rlz=1C1VFKB_enGB657GB658&tbm=isch&tbo=u&source=univ&sa=X&ved=0ahUKEwiZmI-xpaTRAhVIKMAKHUypDz4QsAQITA&biw=866&bih=452#tbm=isch&q=flux+and+induced+emf&imgrc=rd3_kOmysfILDM:
IMO, the signs of dΦ/dt and induced emf E should be opppsite while drawing the graph.

The flux Φ only increases or decreases and increasing Φ gives positive dΦ/dt while decreasing Φ gives a negative dΦ/dt. But induced emf E has two possible directions depending on dΦ/dt and winding direction. Out of these two directions, we can't determine which one is positive and which one is negative. So, I think the correct way to draw the graph of emf is
1)Draw the graph of flux.
2)Compute the magnitude of E using dΦ/dt.
3) Considering the sign of dΦ/dt, attach the opposite sign to the emf E and draw its graph, regardless of its direction.

This means the induced emf should always lag behind the flux by 90°.

Corrections are welcome.

## 1. What is the purpose of drawing flux and induced EMF graphs?

The purpose of drawing these graphs is to visually represent the relationship between flux and induced EMF as described by Faraday's and Lenz's laws. These laws state that a changing magnetic flux through a conductor will induce an electromotive force (EMF) in the conductor, and the direction of the induced EMF will oppose the change in flux.

## 2. How do you plot a flux and induced EMF graph?

To plot a flux and induced EMF graph, you will need to measure the changing flux and induced EMF values at different points in time. The flux can be measured using a fluxmeter, and the induced EMF can be measured using a voltmeter. Then, the flux and induced EMF values can be plotted on a graph with time on the x-axis and flux/induced EMF on the y-axis.

## 3. What does the shape of the flux and induced EMF graph indicate?

The shape of the graph will depend on the type of change in flux. If the flux is increasing, the graph will show a positive slope, indicating a positive induced EMF. If the flux is decreasing, the graph will show a negative slope, indicating a negative induced EMF. The magnitude of the induced EMF can also be determined by the steepness of the slope on the graph.

## 4. How does Lenz's law relate to the direction of the induced EMF?

Lenz's law states that the direction of the induced EMF will always oppose the change in flux that caused it. In other words, if the flux is increasing, the induced EMF will be in the opposite direction of the change in flux. This is why the slope of the induced EMF on the graph will be negative when the flux is increasing.

## 5. What real-life applications use flux and induced EMF graphs?

Flux and induced EMF graphs are commonly used in the study of electromagnetics and in the design of electrical devices, such as generators and transformers. They are also used in industries such as power generation, where understanding the relationship between flux and induced EMF is important for efficient energy production.

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