### Approximation Error of Magnetic Field in a Solenoid**Problem Statement:**Calculate the error in the approximation of the magnetic field \( B = \mu_0 n I \) (or in terms of Coulomb's constant \( k_e \), \( B = \frac{4\pi k_e}{c^2} n I \)) at the center of a solenoid. The solenoid is characterized by the following parameters:- Length: 30 cm- Diameter: 5 cm- Wrapped with \( n \) turns per meter- Carries a current \( I \)**Task:**Determine by how much the approximation \( B = \mu_0 n I \) deviates from the exact expression. Express this deviation as a percentage.**Solution Steps:**1. Consider the parameters of the solenoid (length, diameter, turns per meter, and current).2. Compare the magnetic field approximation to the exact expression.3. Calculate the percentage deviation.4. Enter the percentage result in the provided text box.**Hint Button:**A "Hint" button is provided for assistance in solving the problem.**Answer Section:**A dropdown selection is available to indicate the percentage error compared to the exact expression. Enter your calculation in the text box followed by the percentage symbol \(%\).This content is structured for educational purposes, helping students understand the approximation errors in physical calculations related to magnetic fields in solenoids.

Answered: Image /qna-images/answer/ace89e75-1c1a-442e-933f-01bf0b977ac4.jpg

4Tke By how much is the approximation B = ponI [or in terms of Coulomb's constant ke, B = c2 nI] in error at the center of a solenoid that is 30 cm long, has a diameter of 5 cm, is wrapped withn turns per meter, and carries a current I? Hint Compared to the exact expression, the approximation B HonI is Select an answer v by %3D %.

4Tke By how much is the approximation B = ponI [or in terms of Coulomb's constant ke, B = c2 nI] in error at the center of a solenoid that is 30 cm long, has a diameter of 5 cm, is wrapped withn turns per meter, and carries a current I? Hint Compared to the exact expression, the approximation B HonI is Select an answer v by %3D %.

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

### Approximation Error of Magnetic Field in a Solenoid

**Problem Statement:**

Calculate the error in the approximation of the magnetic field \( B = \mu_0 n I \) (or in terms of Coulomb's constant \( k_e \), \( B = \frac{4\pi k_e}{c^2} n I \)) at the center of a solenoid. The solenoid is characterized by the following parameters:

- Length: 30 cm
- Diameter: 5 cm
- Wrapped with \( n \) turns per meter
- Carries a current \( I \)

**Task:**

Determine by how much the approximation \( B = \mu_0 n I \) deviates from the exact expression. Express this deviation as a percentage.

**Solution Steps:**

1. Consider the parameters of the solenoid (length, diameter, turns per meter, and current).
2. Compare the magnetic field approximation to the exact expression.
3. Calculate the percentage deviation.
4. Enter the percentage result in the provided text box.

**Hint Button:**

A "Hint" button is provided for assistance in solving the problem.

**Answer Section:**

A dropdown selection is available to indicate the percentage error compared to the exact expression. Enter your calculation in the text box followed by the percentage symbol \(%\).

This content is structured for educational purposes, helping students understand the approximation errors in physical calculations related to magnetic fields in solenoids.

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