What is the Correct Method for Finding Induced EMF in a Coil?

Then calculate the angle θ.In summary, the problem involves a 4.0 cm diameter coil with 1000 turns, at rest in the XY plane. The magnetic field in this region is given by B=(0.30i + 0.50t2 k). The goal is to find the induced EMF in the coil at t=2.0 seconds. The equations used are ε=dΦ/dt and Φ=ABcosθ. To solve the problem, the correct diagram must first be drawn, with the coordinate system inside the circle representing the coil. After calculating the angle θ to be 59°, the final result for the induced EMF is 0.00129V k.
  • #1
ReidMerrill
66
2

Homework Statement


A 4.0 cm diameter coil (1000 turns) is at rest in the XY plane. The magnetic field in this region of space is given by B=(0.30i + 0.50t2 k) What is the induced EMF in the coil at t=2.0 seconds

Homework Equations


ε=dΦ/dt
Φ=ABcosθ

The Attempt at a Solution


ε=[/B]d/dt( πr2)(0.03i+0.5t2 k) Cosθ
ε=πr2cosθ *0.5*2t k

Using trig I found θ=59° and plugging in the numbers I got ε=0.00129V k

I assume I did something wrong. Is this anywhere close to the proper method?
 
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  • #2
You need to first sketch the correct diagram! Draw a circle, and position your co-ordinate system inside that circle (the ring) appropriately.
 

1. What is induced EMF in a coil?

Induced EMF (electromotive force) in a coil is a phenomenon in which a changing magnetic field induces a voltage in a coil of wire. This voltage, also known as induced voltage, is created when there is relative motion between a magnetic field and a conductive material, such as a coil of wire.

2. How is induced EMF calculated?

The induced EMF in a coil can be calculated using Faraday's Law, which states that the induced voltage is equal to the rate of change of the magnetic flux through the coil. This can be mathematically represented as E = -N * (∆Φ/∆t), where E is the induced EMF, N is the number of turns in the coil, and ∆Φ/∆t is the change in magnetic flux over time.

3. What factors affect induced EMF in a coil?

The magnitude of induced EMF in a coil is affected by several factors, including the strength of the magnetic field, the number of turns in the coil, the speed of the relative motion between the magnetic field and the coil, and the orientation of the coil with respect to the magnetic field.

4. How is induced EMF used in everyday life?

Induced EMF is used in a variety of applications, such as generators, transformers, and electric motors. It is also used in technologies such as wireless charging and electromagnetic induction stovetops.

5. What are some real-world examples of induced EMF in a coil?

Some common examples of induced EMF in a coil include the ignition coil in a car engine, the transformer used in power distribution, and the generator in a hydroelectric dam. Induced EMF is also used in everyday devices such as electric toothbrushes and wireless phone chargers.

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