Part 2: Dual Coil Experiment:In the following experiment, you will measure the spatial dependence of the magnetic field along thez-axis above a multi-turn coil. Rather than using a constant (DC) current source that would producea static magnetic field, you will use a time-varying, alternating current (AC) source that will producea time-varying magnetic field. The time-varying magnetic field will produce a time-varying magneticflux through a pick-up coil, and you will measure the resulting induced emf (in volts).2.1 Show that the magnitude of the magnetic field B along the positive z-axis through the center of acircular loop that carries a steady current I (see Fig. 1) can be expressed asHOIR²N2(R² + z²)³/2where R is the radius of the loop and N is the number of turns in the current loop.B(z)R=Z2I(5)Figure 1: A circular loop of wire, with N turns, carrying a current I. The magnetic field is given along thepositive z-axis.

According to Biot–Savart’s law, the magnitude of the magnetic field dB is proportional to the…

Show that the magnitude of the magnetic field B along the positive z-axis through the center of a circular loop that carries a steady current I (see Fig. 1) can be expressed as HOIR²N 2(R² + z²)3/2 where R is the radius of the loop and N is the number of turns in the current loop. B(z) =

Show that the magnitude of the magnetic field B along the positive z-axis through the center of a circular loop that carries a steady current I (see Fig. 1) can be expressed as HOIR²N 2(R² + z²)3/2 where R is the radius of the loop and N is the number of turns in the current loop. B(z) =

Glencoe Physics: Principles and Problems, Student Edition

1st Edition

ISBN:9780078807213

Author:Paul W. Zitzewitz

Publisher:Paul W. Zitzewitz

Chapter24: Magnetic Fields

Section: Chapter Questions

Problem 102A

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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

Part 2: Dual Coil Experiment:
In the following experiment, you will measure the spatial dependence of the magnetic field along the
z-axis above a multi-turn coil. Rather than using a constant (DC) current source that would produce
a static magnetic field, you will use a time-varying, alternating current (AC) source that will produce
a time-varying magnetic field. The time-varying magnetic field will produce a time-varying magnetic
flux through a pick-up coil, and you will measure the resulting induced emf (in volts).
2.1 Show that the magnitude of the magnetic field B along the positive z-axis through the center of a
circular loop that carries a steady current I (see Fig. 1) can be expressed as
HOIR²N
2(R² + z²)³/2
where R is the radius of the loop and N is the number of turns in the current loop.
B(z)
R
=
Z
2
I
(5)
Figure 1: A circular loop of wire, with N turns, carrying a current I. The magnetic field is given along the
positive z-axis.

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