# Calculate the induced EMF of a rotating loop

• dainceptionman_02
In summary: To get the sign too, you would need to use trigonometry — and the angle.So if you need the emf at some specific angle, you can’t use the amplitude. And you can’t use ωNBA either. You have to go back to the basic formula: ξ = -N(dΦ/dt).That’s what BvU is telling you. The formula ξ = ωNBA is a special case, for when the angle is such that the emf is at maximum. You were right when you wrote “the instantaneous emf is the amplitude, or ωNBA”. But only for that special case.
dainceptionman_02
Homework Statement
A rectangular loop (area = 0.15m^2) turns in a uniform magnetic field, B=0.20T. When the angle between the field and the normal to the plane of the loop is π/2 rad and increasing at 0.60rad/s, what emf is induced in the loop?
Relevant Equations
ξ=-N(dΦ/dt), Φ=BAcosθ
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.

ξ=-N(dΦ/dt) = -NBA(d/dt)(cosθ) = -NBA(-sinθ)dθ/dt, where dθ/dt=ω, which is 0.60rad/s.

the problem states that initially the angle between the field and the normal to the plane is π/2 rad and increasing at 0.60rad/s, which should mean that initially the flux is zero, because Φ=BAcosθ=BAcos(π/2)=0

now, the amplitude, or the maximum emf induced in the loop is ωNBA = (0.60rad/s)(1)(0.20T)(0.15m^2) = 0.018V, but like i said, i think they are asking something else, but i don't know what?

Hi,
!​

dainceptionman_02 said:
Homework Statement:: A rectangular loop (area = 0.15m^2) turns in a uniform magnetic field, B=0.20T. When the angle between the field and the normal to the plane of the loop is π/2 rad and increasing at 0.60rad/s, what emf is induced in the loop?
Relevant Equations:: ξ=-N(dΦ/dt), Φ=BAcosθ

i think they are asking something else
They are asking the instantaneous emf, for which you have a relevant equation with all factors known ...

 Oh, and: when in doubt, make a sketch !

##\ ##

Steve4Physics, dainceptionman_02, SammyS and 1 other person
BvU said:
They are asking the instantaneous emf, for which you have a relevant equation with all factors known ...

 Oh, and: when in doubt, make a sketch !
i have never seen this before! what do i do, or how do i set it up? thanks!

dainceptionman_02 said:
ξ=-N(dΦ/dt) = -NBA(d/dt)(cosθ) = -NBA(-sinθ)dθ/dt
with all factors known

BvU said:

with all factors known
so the instantaneous emf is the amplitude, or ωNBA?

Make a sketch to understand why !

dainceptionman_02
dainceptionman_02 said:
so the instantaneous emf is the amplitude, or ωNBA?
What do you think is this ξ in the formula shown by BvU? You seem to know it too.

I'd like to add a few words to what @BvU has already said.

dainceptionman_02 said:
so the instantaneous emf is the amplitude, or ωNBA?
EDIT: amplitude = ωNBA. But instantaneous emf means something else.

That's not true in general. (It can be true in special cases.)

When a coil rotates in a magnetic field, the emf produced varies with time. At different times (different angles) during a rotation, the emf can be positive or negative or zero. For a steady angular speed, a graph of emf against time is a sine curve.

The amplitude is the maximum value of |emf|; it is given by ωNBA for a simple setup.

That means if you want the value of emf at some arbitrary moment of time (some arbitrary angle) you can’t use ωNBA.

Of course if the particular angle of interest is, by coincidence, an angle where |emf| is maximum, then ωNBA gives you |emf| but not the sign (+ or -) of the emf.

Last edited:
dainceptionman_02 and TSny

## 1. What is induced EMF?

Induced EMF (electromotive force) is the voltage generated in a conductor when it is exposed to a changing magnetic field. It is a result of Faraday's law of induction, which states that a changing magnetic field will induce a current in a nearby conductor.

## 2. How is induced EMF calculated?

The induced EMF in a rotating loop can be calculated using the formula E = -N(dΦ/dt), where E is the induced EMF, N is the number of turns in the loop, and dΦ/dt is the rate of change of magnetic flux through the loop. This formula can also be written as E = -NBAωsin(ωt), where B is the magnetic field strength, A is the area of the loop, ω is the angular frequency of rotation, and t is time.

## 3. What factors affect the induced EMF in a rotating loop?

The induced EMF in a rotating loop is affected by several factors, including the strength of the magnetic field, the size and shape of the loop, the speed of rotation, and the angle between the magnetic field and the plane of the loop. Additionally, the number of turns in the loop and the material of the conductor can also affect the induced EMF.

## 4. How does the direction of rotation affect the induced EMF?

The direction of rotation does not affect the magnitude of the induced EMF, but it does determine the direction of the current flow. According to Lenz's law, the direction of the induced current will be such that it opposes the change in magnetic flux that caused it. This means that the direction of the induced current will be opposite to the direction of rotation of the loop.

## 5. What is the practical application of calculating induced EMF in a rotating loop?

Calculating induced EMF in a rotating loop is important in understanding and designing devices such as electric generators and motors. These devices use the principle of electromagnetic induction to convert mechanical energy into electrical energy or vice versa. Additionally, induced EMF is also used in various sensors and measurement instruments, such as tachometers and speedometers, to measure the speed of rotation.

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