**Problem: Solenoid Magnetic Field Calculation**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?\[(\mu_0 = 4\pi \times 10^{-7} \, \text{T} \cdot \text{m/A})\]**Explanation:**This problem involves calculating the magnetic field at the center of an ideal solenoid. An ideal solenoid is characterized by:- A uniform magnetic field inside- No magnetic field outsideThe formula for the magnetic field \( B \) inside an ideal solenoid is given by:\[B = \mu_0 \cdot n \cdot I\]where:- \( B \) is the magnetic field,- \( \mu_0 \) is the permeability of free space (\(4\pi \times 10^{-7} \, \text{T} \cdot \text{m/A}\)),- \( n \) is the number of turns per unit length of the solenoid,- \( I \) is the current through the solenoid. Given the data:- Total turns \( N = 200 \)- Current \( I = 2.0 \, \text{A} \)- Length of solenoid \( L = 25 \, \text{cm} = 0.25 \, \text{m} \)Calculate \( n \) as follows:\[n = \frac{N}{L} = \frac{200}{0.25 \, \text{m}}\]Substitute \( n \) and \( I \) into the formula to find \( B \).

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Answered: 8. An ideal solenoid having 200 turns…

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? смо = 4 x 10-7 T·m/A)

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

**Problem: Solenoid Magnetic Field Calculation**

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?

\[
(\mu_0 = 4\pi \times 10^{-7} \, \text{T} \cdot \text{m/A})
\]

**Explanation:**

This problem involves calculating the magnetic field at the center of an ideal solenoid. An ideal solenoid is characterized by:

- A uniform magnetic field inside
- No magnetic field outside

The formula for the magnetic field \( B \) inside an ideal solenoid is given by:

\[
B = \mu_0 \cdot n \cdot I
\]

where:
- \( B \) is the magnetic field,
- \( \mu_0 \) is the permeability of free space (\(4\pi \times 10^{-7} \, \text{T} \cdot \text{m/A}\)),
- \( n \) is the number of turns per unit length of the solenoid,
- \( I \) is the current through the solenoid.

Given the data:
- Total turns \( N = 200 \)
- Current \( I = 2.0 \, \text{A} \)
- Length of solenoid \( L = 25 \, \text{cm} = 0.25 \, \text{m} \)

Calculate \( n \) as follows:
\[
n = \frac{N}{L} = \frac{200}{0.25 \, \text{m}}
\]

Substitute \( n \) and \( I \) into the formula to find \( B \).

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