Magnetic Field inside a Solenoid (Please explain this answer to me)

In summary, the magnetic field of an ideal solenoid can be calculated using the formula: B = µ0 * I * N, where µ0 is the permeability constant (1.257E-6), I is the current, and N is the number of turns. In this problem, the solenoid has a length of 3.0 cm, a radius of 0.50 cm, and 500 turns of wire carrying a current of 2.0 A. Using the given formula, we can calculate the magnetic field to be 4.2 x 10-2 T. It is important to note that the magnetic field is independent of the solenoid's cross-sectional area and only applies to semi
  • #1
Strawberry
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Homework Statement


Q5. A solenoid is 3.0 cm long and has a radius of 0.50 cm. It is wrapped with 500 turns of wire carrying a current of 2.0 A. T


Homework Equations



Magnetic field of an ideal solenoid = permeability constant (1.257E-6) * current * number of turns

The Attempt at a Solution



The given answer is: 4.2 x 10-2 T

I don't understand how to get this answer. From what my book says, the magnetic field is independent of cross-sectional area and only deals with semi-infinite solenoids. Please help!
 
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  • #2
err nvm, I figured it out. I was seriously staring at this thing for two hours and then finally figure it out after I post it ><
 
  • #3


First, it is important to understand what a solenoid is. A solenoid is a cylindrical coil of wire that creates a magnetic field when an electric current is passed through it. The magnetic field inside the solenoid is uniform and parallel to the axis of the solenoid.

To calculate the magnetic field inside a solenoid, we can use the equation B = μ0 * n * I, where B is the magnetic field, μ0 is the permeability constant (a physical constant that describes the magnetic properties of a material), n is the number of turns of wire per unit length, and I is the current.

In this case, we are given the length of the solenoid (3.0 cm), the radius (0.50 cm), the number of turns (500), and the current (2.0 A). To find the magnetic field, we need to first calculate the number of turns per unit length, which is given by n = N/L, where N is the number of turns and L is the length of the solenoid. Plugging in the values, we get n = 500/3.0 = 166.67 turns/cm.

Next, we can plug all the values into the equation B = μ0 * n * I. The permeability constant μ0 is a known value (1.257E-6), so we can simply multiply it by the number of turns per unit length (166.67 turns/cm) and the current (2.0 A). This gives us B = (1.257E-6)(166.67)(2.0) = 4.2 x 10-2 T.

Therefore, the magnetic field inside the solenoid is 4.2 x 10-2 T, as given in the answer. This calculation assumes an ideal solenoid, meaning that the length is much greater than the radius and the magnetic field is uniform inside the solenoid. In reality, the magnetic field may vary slightly due to the finite length and radius of the solenoid, but for practical purposes, this calculation is accurate.
 

Question 1: What is a solenoid?

A solenoid is a coil of wire that is tightly wrapped in a helix shape. It is commonly used in electronic devices and consists of a core, usually made of iron, and an electric current running through the wire.

Question 2: How is a magnetic field created inside a solenoid?

A magnetic field is created inside a solenoid when an electric current flows through the wire. The current creates a magnetic field that runs in the same direction as the current, resulting in a strong magnetic field inside the solenoid.

Question 3: What factors affect the strength of the magnetic field inside a solenoid?

The strength of the magnetic field inside a solenoid is affected by several factors, including the number of turns in the coil, the amount of current flowing through the wire, and the material of the core. Increasing any of these factors will result in a stronger magnetic field.

Question 4: How does the direction of the magnetic field inside a solenoid relate to the direction of the current?

The direction of the magnetic field inside a solenoid is determined by the direction of the electric current flowing through the wire. The magnetic field lines run in the same direction as the current, creating a strong and uniform magnetic field inside the solenoid.

Question 5: What are some practical applications of solenoids?

Solenoids have a wide range of practical applications. They are commonly used in electronic devices such as motors, relays, and speakers. They are also used in medical equipment, security systems, and industrial machinery. Solenoids are essential components in many everyday devices and play a crucial role in modern technology.

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