Can we consider an amperian loop inside a solenoid and if so the i net enclosed by loop is zero which means 0 B inside solenoid but we have B inside it???

Absolutely, we can consider an Amperian loop inside a solenoid, and it's a great way to understand the magnetic field behavior in such a setup. Let's break this down step by step to clarify why the magnetic field inside a solenoid is not zero, even when the net current enclosed by an Amperian loop appears to be zero.

Understanding the Amperian Loop

An Amperian loop is a closed path used in Ampère's Law to calculate the magnetic field generated by electric currents. Ampère's Law states that the line integral of the magnetic field B around a closed loop is proportional to the total current I enclosed by that loop:

∮ B · dl = μ₀ I_enclosed

Considering the Solenoid

A solenoid is essentially a coil of wire that generates a magnetic field when an electric current passes through it. The magnetic field inside an ideal solenoid is uniform and directed along the axis of the solenoid. The key point here is that the magnetic field inside a solenoid is determined by the current flowing through the coils of wire that make up the solenoid.

Applying Ampère's Law

Now, if we take an Amperian loop that lies entirely inside the solenoid, we need to consider the current enclosed by that loop. If the loop is chosen such that it does not enclose any of the current-carrying wires, it might seem at first glance that the enclosed current is zero. However, this is where the concept of the solenoid's structure comes into play.

• The current flowing through the solenoid's coils creates a magnetic field that fills the interior of the solenoid.
• Even if the Amperian loop does not enclose any current directly, the magnetic field inside the solenoid is still a result of the current flowing through the coils.

Magnetic Field Inside the Solenoid

The magnetic field inside an ideal solenoid can be expressed as:

B = μ₀ n I

Where:

• B is the magnetic field strength.
• μ₀ is the permeability of free space.
• n is the number of turns per unit length of the solenoid.
• I is the current flowing through the solenoid.

Thus, even if the Amperian loop does not enclose any current, the magnetic field inside the solenoid is still present due to the current flowing through the coils. The magnetic field lines are concentrated inside the solenoid, leading to a strong and uniform magnetic field.

Visualizing the Concept

Think of the solenoid like a water pipe. The water flowing through the pipe represents the electric current, and the pressure of the water represents the magnetic field. If you place a sensor (the Amperian loop) inside the pipe but not directly in contact with the water, you might not measure the flow directly, but you can still feel the pressure exerted by the water around you. Similarly, the magnetic field exists throughout the interior of the solenoid, even if the Amperian loop does not enclose any current.

In summary, while the net current enclosed by an Amperian loop inside a solenoid might be zero if it does not enclose any turns, the magnetic field inside the solenoid is still non-zero due to the current flowing through the solenoid's coils. This is a fundamental aspect of electromagnetism and highlights the relationship between electric currents and magnetic fields.