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Chapter 13: Problem 2

In Faraday's experiments, what would be the advantage of using coils with many turns?

Short Answer

Expert verified
In Faraday's experiments, using coils with many turns has several advantages including increased induced EMF, improved sensitivity, enhanced efficiency, and better results. This allows for a higher voltage generation, leading to improved detection of smaller changes in magnetic fields and a more accurate understanding of the relationship between changing magnetic fields and induced electromotive force.

Step by step solution

01

Understanding Faraday's Law of Electromagnetic Induction

Faraday's Law states that the electromotive force (EMF) induced in a coil is proportional to the rate of change of magnetic flux through the coil. This can be expressed mathematically as: \(EMF = -N\frac{d\Phi}{dt}\) where \(EMF\) is the induced electromotive force, \(N\) is the number of turns in the coil, \(\Phi\) is the magnetic flux, and \(\frac{d\Phi}{dt}\) is the rate of change of magnetic flux with respect to time.
02

Analyzing the Effect of More Turns in the Coil on Induced EMF

From Faraday's Law, we can see that the induced EMF is directly proportional to the number of turns in the coil (N). This means that, \(EMF \propto N\) When the number of turns increases, the induced EMF also increases.
03

Considering the Advantages of Using Coils with Many Turns

There are several advantages of using coils with more turns in Faraday's experiments: 1. Increased induced EMF: More turns will result in a higher induced EMF for the same change in magnetic flux. This higher voltage can make the effect more noticeable and easier to measure. 2. Improved sensitivity: With a larger induced EMF, the experiment becomes more sensitive to smaller changes in the magnetic field, which may not have been detectable with fewer turns in the coil. 3. Enhanced efficiency: More turns in the coil means more wire is used, which will increase the efficiency of the coil when used in applications such as transformers or generators. 4. Better Results: Coils with many turns are more likely to give better results in terms of a higher induced EMF and a more accurate measurement of the relationship between the changing magnetic field and the induction. In conclusion, using coils with many turns in Faraday's experiments provides several advantages, including increased induced EMF, improved sensitivity, enhanced efficiency, and better results. This helps in understanding the relationship between changing magnetic fields and the induced electromotive force more accurately.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Induced Electromotive Force (EMF)
When you hear about induction in physics, the induced electromotive force (EMF) is a key player. EMF is the voltage generated in a coil due to changing magnetic conditions.
Faraday's Law of Electromagnetic Induction provides a clear picture:
  • The induced EMF is proportional to the rate at which the magnetic flux changes through the coil.
  • Mathematically, it is represented as \(EMF = -N\frac{d\Phi}{dt}\), where \(N\) is the number of turns and \(\Phi\) is the magnetic flux.
The negative sign indicates the direction of the induced EMF, as given by Lenz's law, which states that it opposes the change causing it. By understanding this law, you can better appreciate how a coil's design can affect how much EMF is induced.
Magnetic Flux
Magnetic Flux is the total magnetic field passing through a given area. Think of it as the number of magnetic field lines that penetrate a surface.
Here's what to know about magnetic flux:
  • It's measured in Webers (Wb) and depends on the strength of the magnetic field and the area it passes through.
  • The mathematical representation is \(\Phi = B \cdot A \cdot \cos(\theta)\), where \(B\) is the magnetic field strength, \(A\) is the area, and \(\theta\) is the angle between them.
  • Changing the magnetic flux within a coil leads to the induction of EMF. Faster changes result in a higher EMF.
Understanding magnetic flux helps in comprehending how different factors like the field strength, area, and angle influence the induction process.
Coil Turns
The number of turns in a coil is a simple yet powerful factor in electromagnetic induction. More turns in a coil mean more opportunities for magnetic field interactions.
  • The induced EMF increases directly with more coil turns (\(EMF \propto N\)).
  • Each additional turn adds to the total magnetic flux change, leading to a stronger induced EMF.
  • In practical terms, more coil turns mean higher sensitivity and efficiency, making your equipment more reliable in detecting changes.
Increasing the coil turns in experiments is a smart choice for clearer results, as it maximizes the EMF generated even with small changes in magnetic fields.

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Most popular questions from this chapter

Shown below is a conducting rod that slides along metal rails. The apparatus is in a uniform magnetic field of strength \(0.25 \mathrm{T}\), which is directly into the page. The rod is pulled to the right at a constant speed of \(5.0 \mathrm{m} / \mathrm{s}\) by a force \(\overrightarrow{\mathbf{F}}\). The only significant resistance in the circuit comes from the \(2.0-\Omega\) resistor shown. (a) What is the emf induced in the circuit? (b) What is the induced current? Does it circulate clockwise or counter clockwise? (c) What is the magnitude of \(\overrightarrow{\mathbf{F}}\) ? (d) What are the power output of \(\overrightarrow{\mathbf{F}}\) and the power dissipated in the resistor?

A circular copper disk of radius \(7.5 \mathrm{cm}\) rotates at 2400 rpm around the axis through its center and perpendicular to its face. The disk is in a uniform magnetic field \(\overrightarrow{\mathbf{B}}\) of strength \(1.2 \mathrm{T}\) that is directed along the axis. What is the potential difference between the rim and the axis of the disk?

The armature and field coils of a series-wound motor have a total resistance of \(3.0 \Omega\). When connected to a 120-V source and running at normal speed, the motor draws 4.0 A. (a) How large is the back emf? (b) What current will the motor draw just after it is turned on? Can you suggest a way to avoid this large initial current?

A 2-turn planer loop of flexible wire is placed inside a long solenoid of \(n\) turns per meter that carries a constant current \(I_{0} .\) The area \(A\) of the loop is changed by pulling on its sides while ensuring that the plane of the loop always remains perpendicular to the axis of the solenoid. If \(n=500\) turns per meter, \(I_{0}=20 \mathrm{A},\) and \(A=20 \mathrm{cm}^{2}\) what is the emf induced in the loop when \(d A / d t=100 ?\)

The current in a long solenoid of radius \(3 \mathrm{cm}\) and 20 turns/cm is varied with time at a rate of \(2 \mathrm{A} / \mathrm{s}\). Find the electric field at a distance of \(4 \mathrm{cm}\) from the center of the solenoid.
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