What Is the Magnetic Field at the Center of a Solenoid?

[kiltfish]

This is driving me insane. This is all I can think of to do, and my teacher said it was wrong.

A solenoid of length 0.25m and radius 0.025m is comprised of 440 turns of wire. Determine the magnitude of the magnetic field at the center of the solenoid when it carries a current of 12 A.



B=u(N/L)I

B=0.0265 T

 

[gneill]

I don't see what's wrong with that. Unless your teacher wants you to compute the magnetic flux density rather than the field strength?

 

[kiltfish]

Apparently he insists that the answer is 2.21 x 10^-3 T. I don't think that's what you would get calculating for the magnetic flux density, but if it is, how can you tell he's asking for that is the problem? I gave you the exact words he asked.

 

[gneill]

Let's see how his answer compares to the one you (and I) calculate:

(2.654 x 10^-2 T)/(2.21 x 10^-3 T) = 12.0

His answer seems to be 1/12 of the value that we think it should be. Could it be that he wanted the field strength per amp of current?

 

[rwisz]

First of all, I want to assure you that feeling frustrated and overwhelmed by a scientific concept is completely normal and understandable. It takes time and practice to fully understand and apply scientific principles. That being said, let's break down this problem and see if we can help you understand the concept of magnetic fields in a solenoid.

A solenoid is a type of electromagnet that consists of a coil of wire wrapped around a cylindrical core. When an electric current flows through the wire, it creates a magnetic field inside the solenoid.

In this problem, we are given the length, radius, and number of turns of the solenoid, as well as the current flowing through it. To calculate the magnetic field at the center of the solenoid, we can use the equation B=u(N/L)I, where B is the magnetic field, u is the permeability of the material inside the solenoid (usually air or vacuum), N is the number of turns, L is the length of the solenoid, and I is the current.

Plugging in the given values, we get B=u(440/0.25)12. Now, u is a constant value that depends on the material inside the solenoid. For air or vacuum, u is equal to 4πx10^-7 Tm/A. So, substituting that in our equation, we get B=(4πx10^-7)(440/0.25)12.

Simplifying, we get B=0.0265 T, which is the magnitude of the magnetic field at the center of the solenoid. This means that if you were to place a compass at the center of the solenoid, the needle would point towards the north-south direction with a strength of 0.0265 T.

I hope this explanation helps you understand the concept of magnetic fields in a solenoid better. Remember, don't get discouraged if you don't understand something right away. Keep practicing and asking questions, and you will eventually master it. Good luck!