Current of Coil, and Emf of Coil.

In summary, when a magnetic field perpendicular to the plane of a single-turn circular coil induces an emf of 0.91 V and a current of 3.2 A, reforming the wire into a single-turn square coil with the same magnetic field and changing at the same rate will result in an induced emf of 0.72 V and a current of 2.5 A due to the change in loop area.
  • #1
rcmango
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Homework Statement



A magnetic field is perpendicular to the plane of a single-turn circular coil. The magnitude of the field is changing, so that an emf of 0.91 V and a current of 3.2 A are induced in the coil. The wire is the re-formed into a single-turn square coil, which is used in the same magnetic field (again perpendicular to the plane of the coil and with a magnitude changing at the same rate).

What emf and current are induced in the square coil?

Homework Equations



L = 2*pi*r, A = L/4*pi, A = L^2/16

The Attempt at a Solution



Okay i know the lengths are the same for the circular coil and the square coil. Oh and the form has changed.

So A1/A2 = (L^2/4*pi) / (L^2/16) = 16/4*pi

and for the current i could use I2 = V2/R

and I'm not sure but i think R = V1/I1 ?

I have a lot of help so far, not sure what the final answer is, anyone?
 
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  • #2
A complete solution is offered.

Faraday's law tells us that an emf is induced in a loop when the magnetic flux passing through the loop changes. In this case we have a changing magnetic field that is the same in both cases, and a change of loop area due to a change in the geometry of the loop. Only the magnetic field changes; the area of each loop is fixed.

When area is fixed, Faraday's law is:

##emf = A \frac{ΔB}{Δt}##

where ##A## is the loop area and ##B## is the magnetic field strength. ##\frac{ΔB}{Δt}## is the same for both scenarios. What is different is the loop area. Forming ratio for the two cases the changing flux cancels:

##\frac{emf_2}{emf_1} = \frac{A_2}{A_1}##

Apparently we need to look into the ratio of the loop areas.

The length of wire used to form the loop is the same in each case (which means its electrical resistance will be the same, too, which will be important later). So we want the areas in terms of the perimeter, L.

For a circular loop the perimeter is ##L = 2 \pi r## and the area is ##A = \pi r^2## Combining them gives:

##A_1 = \frac{L^2}{4 \pi}##

And for the square loop each side will have length L/4, so

##A_2 = \frac{L^2}{16}##

Giving us the ratio of areas:

##\frac{A_2}{A_1} = \frac{\pi}{4}##

Now returning to Faraday, our emf for the square loop will be:

##emf_2 = emf_1\frac{A_2}{A_1} = (0.91~V)\frac{\pi}{4} = 0.72~V##

With the same resistance the current will be proportional to the emf. So the current will be:

##I_2 = I_1 \frac{emf_2}{emf_1} = I_1 \frac{A_2}{A_1} = (3.2~A) \frac{\pi}{4} = 2.5~A##
 

What is current of coil?

The current of coil refers to the flow of electric charge through a coil of wire. It is measured in amperes (A) and can be either direct current (DC) or alternating current (AC).

What factors affect the current of coil?

The current of coil is affected by the voltage applied, the resistance of the coil, and the number of turns in the coil. Increasing the voltage or decreasing the resistance will result in an increase in current, while increasing the number of turns will decrease the current.

What is the emf of coil?

The emf (electromotive force) of a coil is the energy per unit charge that is supplied by a source, such as a battery, to maintain a current through the coil. It is measured in volts (V).

How is emf of coil related to current of coil?

The emf of a coil is directly proportional to the current flowing through it. This means that as the current increases, the emf also increases. However, the resistance of the coil can also affect the relationship between emf and current.

How can the emf of coil be calculated?

The emf of a coil can be calculated using the formula emf = -N(dΦ/dt), where N is the number of turns in the coil and dΦ/dt is the rate of change of the magnetic flux through the coil. This formula is based on Faraday's Law of Induction, which states that a changing magnetic field can induce an emf in a circuit.

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