### 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.### QuestionWhen 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 VoltageThe 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.

The field due to outer coil in place of inner coil is, B=μ04π2πIR1N1 Since the flux through inner…

Inner coil, radius R2 with N2 turns measure voltage Outer coil, radius R1 with N1 turns, AI/At = 5 amps/second We make a simple metal detector out of two circular coils of wire. The inner coil (radius R2, number of turns N2) is much much smaller than the outer coil (radius R1, number of turns N1), so you can assume the magnetic field is constant over the inner coil. We drive the outer coil with a current that increases at 5 amps/second. If there is no metal around, how much voltage is induced on the inner coil and how do you know? 1.

Inner coil, radius R2 with N2 turns measure voltage Outer coil, radius R1 with N1 turns, AI/At = 5 amps/second We make a simple metal detector out of two circular coils of wire. The inner coil (radius R2, number of turns N2) is much much smaller than the outer coil (radius R1, number of turns N1), so you can assume the magnetic field is constant over the inner coil. We drive the outer coil with a current that increases at 5 amps/second. If there is no metal around, how much voltage is induced on the inner coil and how do you know? 1.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Magnetic Field Of Coaxial Cable

The word coaxial means same axis. So for a long straight cable to be coaxial, it must have concentric cylindrical shaped conductor around it. Coaxial cable (popularly called ‘coax’) has various applications ranging from current conductors to radiofrequency signal transmitters. This cable has lower emission losses and provides protection from electromagnetic interference which allows signals with less power to transmit over longer distances.For example, currents produced in the pickup of a stereo turntable generally travel to the amplifier through a coaxial cable.The self-inductance of a coaxial cable is another important characteristic, because it influences the propagation of electrical signals in the cable.

Question

### 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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