# EMF in loop, given magnetic field

• RKOwens4
In summary: In the first problem the flux is a function of the net electric current through the coil. In the second problem the flux is a function of the magnetic field only. The electric current in the coil doesn't change with time. So the EMF in the second problem has to be a function of the magnetic field only, which is what the first equation gives.
RKOwens4

## Homework Statement

In the figure below, a circular loop of wire 12 cm in diameter (seen edge on) is placed with its normal at an angle θ = 30° with the direction of a uniform magnetic field B of magnitude 0.60 T. The loop is then rotated so that N rotates in a cone about the field direction at the rate 160 rev/min; angle θ remains unchanged during the process. What is the emf induced in the loop?

Figure: http://imageshack.us/photo/my-images/854/webassign.jpg/

## Homework Equations

EMF = BAcos(theta)

or

EMF = d(BAcos(theta))/dt

## The Attempt at a Solution

I converted 160 rev/min to rev/sec and then to rad/sec, getting 16.755 rad/sec. I then plugged the given data into the 2nd equation above (trying both positive and negative signs) and it's still incorrect. Any help would be appreciated.

Interesting. The EMF is proportional to the change in flux through the loop. Is there a change? You have the flux as BAcos(theta), which looks correct to me. The B is constant. The A is constant. So is theta. Looks like the flux is constant, so its derivative will be zero.

I'm confused. Are you saying the EMF is zero? I only have one guess left before the problem is marked wrong.

Anyone have any ideas?

Yes, it looks like EMF = 0 to me. There are some B field lines cutting through the wire, but it looks like an equal number cutting in and out, so that approach also yields zero for the EMF.

That was the right answer, but could you please explain the reasoning again? Is it that magnetic flux has to be increasing/decreasing to create an EMF, and if the flux is constant then EMF is zero? Because I had another homework problem which I already solved that said, "An electric generator contains a coil of 110 turns of wire formed into a rectangular loop 60.0 cm by 30.0 cm, placed entirely in a uniform magnetic field with magnitude B = 3.50 T and with B initially perpendicular to the coil's plane. What is the maximum value of the emf produced when the coil is spun at 1000 rev/min about an axis perpendicular to B?" For this one I just used the formula EMF=NABomega (where omega = 104.7) and got the correct answer of 7,257 V. Can you explain why the two problems are different?

In one problem the net flux linking the loop changes with time. In the other it doesn't.

## 1. What is EMF?

EMF stands for electromagnetic force, which is the force that causes charged particles to move in response to a magnetic field. It is the driving force behind the movement of electricity.

## 2. How is EMF related to magnetic fields?

EMF is directly related to magnetic fields, as a change in magnetic field can induce an electric current, creating an EMF. This phenomenon is known as electromagnetic induction.

## 3. What is the formula for calculating EMF in a loop given a magnetic field?

The formula for calculating EMF in a loop is EMF = -N(dΦ/dt), where N is the number of turns in the loop and dΦ/dt is the rate of change of magnetic flux through the loop. This is known as Faraday's Law of Induction.

## 4. How does the strength of the magnetic field affect the EMF in a loop?

The strength of the magnetic field directly affects the magnitude of the induced EMF in a loop. A stronger magnetic field will result in a larger EMF, while a weaker magnetic field will result in a smaller EMF.

## 5. What are some real-world applications of EMF in a loop given a magnetic field?

EMF in a loop given a magnetic field is the principle behind many electrical devices, such as generators and motors. It is also used in various technologies, such as wireless charging and magnetic levitation trains.

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