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Chapter 28: Problem 46

A current of \(2.00 \mathrm{~A}\) is flowing through a 1000 -turn solenoid of length \(L=40.0 \mathrm{~cm} .\) What is the magnitude of the magnetic field inside the solenoid?

Short Answer

Expert verified
Answer: The magnitude of the magnetic field inside the solenoid is approximately \(6.28 脳 10^{-4} \, T\).

Step by step solution

01

Identify given variables and constants

We are given the following information: - Current (\(I\)): \(2.00 \, A\) - Number of turns (\(N\)): \(1000\) - Length of the solenoid (\(L\)): \(40.0 \, cm = 0.4 \, m\) - Permeability of free space (\(\mu_0\)): \(4 \pi 脳 10^{-7} \, Tm/A\)
02

Calculate the number of turns per unit length (n)

To find the number of turns per unit length (n), we'll use the formula \(n = \frac{N}{L}\). Using the given values: $$ n = \frac{1000}{0.4} = 2500 \, turns/m $$
03

Calculate the magnitude of the magnetic field (B)

Now, we can use the formula for the magnetic field inside a solenoid: \(B = \mu_0 n I\). Plug in the values and calculate B: $$ B = (4 \pi 脳 10^{-7} \, Tm/A) 脳 (2500 \, turns/m) 脳 (2 \, A) \\ B = (4 \pi 脳 10^{-7} \, Tm/A) 脳 5000 \, A/m \\ B \approx 6.28 脳 10^{-4} \, T $$ So, the magnitude of the magnetic field inside the solenoid is approximately \(6.28 脳 10^{-4} \, T\).

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Most popular questions from this chapter

Two identical coaxial coils of wire of radius \(20.0 \mathrm{~cm}\) are directly on top of each other, separated by a 2.00 -mm gap. The lower coil is on a flat table and has a current \(i\) in the clockwise direction; the upper coil carries an identical current and has a mass of \(0.0500 \mathrm{~kg} .\) Determine the magnitude and the direction that the current in the upper coil has to have to keep the coil levitated at its current height.

Two long, parallel wires separated by a distance, \(d\), carry currents in opposite directions. If the left-hand wire carries a current \(i / 2,\) and the right-hand wire carries a current \(i\), determine where the magnetic field is zero.

A particle detector utilizes a solenoid that has 550 turns of wire per centimeter. The wire carries a current of 22 A. A cylindrical detector that lies within the solenoid has an inner radius of \(0.80 \mathrm{~m} .\) Electron and positron beams are directed into the solenoid parallel to its axis. What is the minimum momentum perpendicular to the solenoid axis that a particle can have if it is to be able to enter the detector?

You are standing at a spot where the magnetic field of the Earth is horizontal, points due northward, and has magnitude \(40.0 \mu \mathrm{T}\). Directly above your head, at a height of \(12.0 \mathrm{~m},\) a long, horizontal cable carries a steady \(\mathrm{DC}\) current of 500.0 A due northward. Calculate the angle \(\theta\) by which your magnetic compass needle is deflected from true magnetic north by the effect of the cable. Don't forget the sign of \(\theta-\) is the deflection eastward or westward?

A long solenoid (diameter of \(6.00 \mathrm{~cm}\) ) is wound with 1000 turns per meter of thin wire through which a current of 0.250 A is maintained. A wire carrying a current of 10.0 A is inserted along the axis of the solenoid. What is the magnitude of the magnetic field at a point \(1.00 \mathrm{~cm}\) from the axis?
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