**Problem:**A 200-turn solenoid with a length of 20 cm and a diameter of 2 cm. When a 5-A current passes through the solenoid, find the magnetic field within the solenoid.**Solution:**To find the magnetic field within the solenoid, we can use the formula for the magnetic field inside a solenoid:\[ B = \mu_0 \times n \times I \]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,- \( I \) is the current passing through the solenoid.First, calculate the number of turns per unit length (\( n \)):\[ n = \frac{\text{Number of turns}}{\text{Length of the solenoid}} = \frac{200}{0.2 \, \text{m}} = 1000 \, \text{turns/m} \]Substitute the values into the formula:\[ B = (4\pi \times 10^{-7}) \times 1000 \times 5 \]\[ B = 2\pi \times 10^{-3} \]\[ B \approx 6.28 \times 10^{-3} \, \text{T} \]Thus, the magnetic field within the solenoid is approximately \( 6.28 \, \text{mT} \).

Given data The number of turns in the solenoid is N = 200 turns. The length of the solenoid is l =…

Answered: 2. A 200-turn solenoid with length of…

2. A 200-turn solenoid with length of 20 cm and diameter of 2 cm. When a 5-A current passes through the solenoid, find the magnetic field within the solenoid.

College Physics

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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:**

A 200-turn solenoid with a length of 20 cm and a diameter of 2 cm. When a 5-A current passes through the solenoid, find the magnetic field within the solenoid.

**Solution:**

To find the magnetic field within the solenoid, we can use the formula for the magnetic field inside a solenoid:

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

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,
- \( I \) is the current passing through the solenoid.

First, calculate the number of turns per unit length (\( n \)):

\[ n = \frac{\text{Number of turns}}{\text{Length of the solenoid}} = \frac{200}{0.2 \, \text{m}} = 1000 \, \text{turns/m} \]

Substitute the values into the formula:

\[ B = (4\pi \times 10^{-7}) \times 1000 \times 5 \]

\[ B = 2\pi \times 10^{-3} \]

\[ B \approx 6.28 \times 10^{-3} \, \text{T} \]

Thus, the magnetic field within the solenoid is approximately \( 6.28 \, \text{mT} \).

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