College Physics
College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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### Simple Metal Detector Using Coils

**Diagram Description:**

- The diagram consists of two circular coils of wire.
- **Inner Coil**: 
  - Labeled "Inner coil, radius R2 with N2 turns".
  - Used to measure voltage.
  - Significantly smaller than the outer coil.
  
- **Outer Coil**:
  - Labeled "Outer coil, radius R1 with N1 turns, ΔI/Δt = 5 amps/second".
  - Current increases at a rate of 5 amps per second.

**Concept Explanation:**

We construct a simple metal detector using two circular wire coils. The inner coil, which has a radius of R2 and N2 number of turns, is much smaller than the outer coil (with radius R1 and N1 turns). This size difference allows us to assume the magnetic field remains constant over the inner coil.

### Question

When the outer coil is driven with an increasing current (5 amps/second), and there is no metal present, how much voltage is induced in the inner coil and why?

### Understanding the Induced Voltage

The voltage induced in the inner coil can be determined using Faraday's Law of electromagnetic induction, which states:

\[
\text{Induced Voltage} (\epsilon) = -N \frac{\Delta \Phi}{\Delta t}
\]

- \(N\) is the number of turns in the coil.
- \(\Delta \Phi\) is the change in magnetic flux.
- \(\Delta t\) is the change in time.

Given that the rate of change of current (ΔI/Δt) is 5 amps/second in the outer coil, this change in magnetic field induces a voltage in the smaller inner coil. The voltage measured depends on the number of turns and the rate of change of the magnetic field passing through it.

This simulation helps in understanding the basic principle of metal detectors and electromagnetic induction.
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Transcribed Image Text:### Simple Metal Detector Using Coils **Diagram Description:** - The diagram consists of two circular coils of wire. - **Inner Coil**: - Labeled "Inner coil, radius R2 with N2 turns". - Used to measure voltage. - Significantly smaller than the outer coil. - **Outer Coil**: - Labeled "Outer coil, radius R1 with N1 turns, ΔI/Δt = 5 amps/second". - Current increases at a rate of 5 amps per second. **Concept Explanation:** We construct a simple metal detector using two circular wire coils. The inner coil, which has a radius of R2 and N2 number of turns, is much smaller than the outer coil (with radius R1 and N1 turns). This size difference allows us to assume the magnetic field remains constant over the inner coil. ### Question When the outer coil is driven with an increasing current (5 amps/second), and there is no metal present, how much voltage is induced in the inner coil and why? ### Understanding the Induced Voltage The voltage induced in the inner coil can be determined using Faraday's Law of electromagnetic induction, which states: \[ \text{Induced Voltage} (\epsilon) = -N \frac{\Delta \Phi}{\Delta t} \] - \(N\) is the number of turns in the coil. - \(\Delta \Phi\) is the change in magnetic flux. - \(\Delta t\) is the change in time. Given that the rate of change of current (ΔI/Δt) is 5 amps/second in the outer coil, this change in magnetic field induces a voltage in the smaller inner coil. The voltage measured depends on the number of turns and the rate of change of the magnetic field passing through it. This simulation helps in understanding the basic principle of metal detectors and electromagnetic induction.
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