### Educational Content#### Problem 7A very long thin wire produces a magnetic field of \(0.002 \times 10^{-4}\, T\) at a distance of \(1.0\, mm\) from the wire. What is the magnitude of the current?\[(\mu_0 = 4\pi \times 10^{-7}\, T \cdot m/A)\]Options:a) 1.0 mA b) 2.0 mA c) 4000 mA d) 3100 mA #### Problem 8An ideal solenoid having 200 turns and carrying a current of \(2.0\, A\) is \(25\, cm\) long. What is the magnitude of the magnetic field at the center of the solenoid?\[(\mu_0 = 4\pi \times 10^{-7}\, T \cdot m/A)\]### Explanation- **Magnetic Field by a Wire (Problem 7):** This problem involves calculating the current in a long straight wire based on the magnetic field and distance from the wire using the formula for the magnetic field around a wire. - **Magnetic Field in a Solenoid (Problem 8):** The problem requires calculating the magnetic field at the center of a solenoid, using the number of turns, the current, and the length of the solenoid. Both problems require understanding of magnetic fields in various configurations, specifically Ampère's law and the Biot-Savart law for long straight wires, and the formula for solenoids.

Given data: Magnetic field (B) = 0.002×10-4 T Distance (r) = 1.0 mm = 1.0×10-3 m μ0 = 4π×10-4 T.m/A…

7. A very long thin wire produces a magnetic field of 0.002 x 10-4 T at a distance of 1.0 mm from the wire. What is the magnitude of the current? (Ho = 4 x 10-7 T.m/A) a) 1.0 mA b) 2.0 mA c) 4000 mA d) 3100 mA

7. A very long thin wire produces a magnetic field of 0.002 x 10-4 T at a distance of 1.0 mm from the wire. What is the magnitude of the current? (Ho = 4 x 10-7 T.m/A) a) 1.0 mA b) 2.0 mA c) 4000 mA d) 3100 mA

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

### Educational Content

#### Problem 7
A very long thin wire produces a magnetic field of \(0.002 \times 10^{-4}\, T\) at a distance of \(1.0\, mm\) from the wire. What is the magnitude of the current?
\[
(\mu_0 = 4\pi \times 10^{-7}\, T \cdot m/A)
\]
Options:
a) 1.0 mA
b) 2.0 mA
c) 4000 mA
d) 3100 mA

#### Problem 8
An ideal solenoid having 200 turns and carrying a current of \(2.0\, A\) is \(25\, cm\) long. What is the magnitude of the magnetic field at the center of the solenoid?
\[
(\mu_0 = 4\pi \times 10^{-7}\, T \cdot m/A)
\]

### Explanation
- **Magnetic Field by a Wire (Problem 7):** This problem involves calculating the current in a long straight wire based on the magnetic field and distance from the wire using the formula for the magnetic field around a wire.

- **Magnetic Field in a Solenoid (Problem 8):** The problem requires calculating the magnetic field at the center of a solenoid, using the number of turns, the current, and the length of the solenoid.

Both problems require understanding of magnetic fields in various configurations, specifically Ampère's law and the Biot-Savart law for long straight wires, and the formula for solenoids.

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