How To Find Magnetic Field Of Solenoid: Direction, Inside, Outside, Center, Several Facts

How to Find Magnetic Field of Solenoid

In this blog post, we will delve into the fascinating world of solenoids and discover how to find the magnetic field they produce. Understanding the concept of solenoids and the importance of magnetic field in them is essential before we dive into the calculations. So, let’s get started!

Understanding the Concept of Solenoid

A solenoid is a long, cylindrical coil of wire that is tightly wound in a helical shape. It resembles a spring, and when an electric current flows through it, it generates a magnetic field. Solenoids are widely used in various applications, including electromagnets, transformers, and inductors.

Importance of Magnetic Field in a Solenoid

The magnetic field produced by a solenoid is of great significance. It allows solenoids to create a magnetic force that can attract or repel objects, and it forms the basis for their functionality in many devices. Understanding and calculating the magnetic field of a solenoid is crucial to harnessing its power.

Calculating Magnetic Field Inside a Solenoid

Now, let’s focus on finding the magnetic field inside a solenoid. The magnetic field inside a solenoid is relatively uniform and parallel to the axis of the solenoid. To calculate it, we can use a simple formula.

The Formula for Magnetic Field Due to a Solenoid

The formula to calculate the magnetic field inside a solenoid is given by:

$B = \mu_0 \cdot n \cdot I$

Where:
– (B) is the magnetic field strength,
– (mu_0) is the permeability of free space $mu_0 = 4\pi \times 10^{-7} \, \text{T m/A}$ ,
– (n) is the number of turns per unit length,
– (I) is the current flowing through the solenoid.

Determining the Magnitude of the Magnetic Field Inside the Solenoid

To find the magnitude of the magnetic field inside the solenoid, we need to know the number of turns per unit length and the current flowing through the solenoid. Let’s consider an example to illustrate this.

Example: Suppose we have a solenoid with a length of 0.5 meters, 500 turns, and a current of 2 amperes. We can calculate the magnetic field inside the solenoid using the formula mentioned earlier.

Using the formula, we have:

$B = (4\pi \times 10^{-7} \, \text{T m/A}) \times (500 \, \text{turns/m}) \times (2 \, \text{A})$

Simplifying this equation, we find that the magnetic field inside the solenoid is approximately 0.00628 Tesla.

Worked Out Examples on Calculating Magnetic Field Inside a Solenoid

Let’s work through a few more examples to solidify our understanding.

Example 1: A solenoid has a length of 0.2 meters, 100 turns per meter, and a current of 0.5 amperes. Calculate the magnetic field inside the solenoid.

Using the formula, we have:

$B = (4\pi \times 10^{-7} \, \text{T m/A}) \times (100 \, \text{turns/m}) \times (0.5 \, \text{A})$

Simplifying this equation, we find that the magnetic field inside the solenoid is approximately 0.00314 Tesla.

Example 2: Consider a solenoid with a length of 0.3 meters, 200 turns per meter, and a current of 1 ampere. Calculate the magnetic field inside the solenoid.

Using the formula, we have:

$B = (4\pi \times 10^{-7} \, \text{T m/A}) \times (200 \, \text{turns/m}) \times (1 \, \text{A})$

Simplifying this equation, we find that the magnetic field inside the solenoid is approximately 0.02513 Tesla.

These examples demonstrate how to calculate the magnetic field inside a solenoid using the given formula.

Determining Magnetic Field Outside a Solenoid

While the magnetic field inside a solenoid is relatively strong, the magnetic field outside the solenoid is negligible. This is because the magnetic field lines produced by the currents flowing through neighboring loops of the solenoid cancel each other out. Therefore, the magnetic field outside a solenoid is considered to be practically zero.

Why Magnetic Field Outside a Solenoid is Negligible

The cancellation of magnetic field lines outside the solenoid occurs due to the equal and opposite magnetic field contributions from neighboring loops. This phenomenon is called “self-cancellation” and results in a negligible magnetic field outside the solenoid.

Mathematical Explanation for Negligible Magnetic Field Outside a Solenoid

Mathematically, we can express the cancellation effect as follows:

$B_{\text{outside}} = 0$

This equation confirms that the magnetic field outside a solenoid is indeed negligible.

Describing the Magnetic Field of a Solenoid

Image by Geek3 – Wikimedia Commons, Wikimedia Commons, Licensed under CC BY-SA 4.0.

The magnetic field inside a solenoid is relatively uniform and parallel to the axis of the solenoid. This uniformity is crucial for many applications that rely on solenoids. However, the magnetic field at the ends of a solenoid differs from the uniform field inside.

The Uniformity of Magnetic Field Inside a Solenoid

Inside a solenoid, the magnetic field lines are parallel and evenly spaced. This uniformity is due to the consistent direction of the current flowing through each loop of the solenoid. The field lines follow a straight path along the solenoid’s axis, creating a strong and uniform magnetic field.

The Variation of Magnetic Field at the Ends of a Solenoid

At the ends of a solenoid, the magnetic field lines curve outward from the solenoid and become less uniform. This deviation occurs because the field lines near the ends experience a different distribution of magnetic forces compared to those in the center. It’s important to consider this variation when designing and utilizing solenoids.

Finding the Magnetic Field at the Center of a Solenoid

The magnetic field at the center of a solenoid is an intriguing topic. Theoretical explanations can help us understand this phenomenon, and we can also calculate the magnetic field at the center using a formula.

Theoretical Explanation of Magnetic Field at the Center

At the center of a solenoid, the magnetic field lines are parallel to the axis of the solenoid and perpendicular to the ends. This orientation occurs because the magnetic field lines produced by the current-carrying loops add up constructively at the center, resulting in a strong and uniform magnetic field.

Mathematical Calculation of Magnetic Field at the Center of a Solenoid

To calculate the magnetic field at the center of a solenoid, we can use the formula:

$B_{\text{center}} = \mu_0 \cdot n \cdot I$

The variables in this formula have the same meanings as mentioned earlier. By plugging in the appropriate values, we can determine the magnetic field at the center of a solenoid.

Understanding how to find the magnetic field of a solenoid is essential for grasping the principles behind its operation. By following the formulas and calculations provided, we can determine the magnetic field inside and at the center of a solenoid. Remember, the magnetic field inside a solenoid is relatively uniform, while the field outside is negligible. With this knowledge, we can explore the fascinating applications and potential of solenoids in various fields.

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AKSHITA MAPARI

Hi, I’m Akshita Mapari. I have done M.Sc. in Physics. I have worked on projects like Numerical modeling of winds and waves during cyclone, Physics of toys and mechanized thrill machines in amusement park based on Classical Mechanics. I have pursued a course on Arduino and have accomplished some mini projects on Arduino UNO. I always like to explore new zones in the field of science. I personally believe that learning is more enthusiastic when learnt with creativity. Apart from this, I like to read, travel, strumming on guitar, identifying rocks and strata, photography and playing chess.