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A solenoid is basically a coil of wire, which generates a magnetic field when an electric current is passed through it. The strength of this magnetic field inside a long solenoid can be determined by the formula \( B = \mu_0 n I_s \). Here, \( \mu_0 \) represents the permeability of free space, a constant value \( (4\pi \times 10^{-7} \, \text{ Tm/A}) \).
The term \( n \) stands for the number of turns per unit length of the solenoid, which in this case is \( 1400 \, \text{ turns/m} \), and \( I_s \) is the current flowing through the solenoid, given as \( 3.5 \, \text{ A} \).
The magnetic field is uniform inside the solenoid and this uniformity is what makes solenoids quite useful in various applications, such as electromagnets or inductors in electronic circuits.

Ampere's Law relates the magnetic field around a closed loop to the electric current passing through the loop. It is represented mathematically as \( \oint \mathbf{B} \cdot d\mathbf{l} = \mu_0 I_\text{enc} \), where \( \mathbf{B} \) is the magnetic field, \( d\mathbf{l} \) is a differential element of the path, and \( I_\text{enc} \) is the current enclosed by the path.
In the context of a solenoid, Ampere's Law helps illustrate how the magnetic field inside the solenoid relates to the current passing through it. The magnetic field is directly proportional to the product of the current and the number of turns per unit length of the solenoid.
Understanding Ampere's Law is crucial when analyzing magnetic fields in solenoids since it provides a theoretical basis for calculating the field strength just by knowing the design parameters of the solenoid and the current it carries.

Solving physics problems, like the one involving solenoids and coils, requires a clear understanding of the formulas and concepts involved. Breaking down the problem into smaller steps makes it more manageable:

• Identify given values and unknowns.
• Choose suitable formulas related to magnetic fields and forces.
• Perform calculations methodically step by step.
• Make sure units are consistent across all calculations.

Analyzing each part of an equation and understanding its physical application can simplify complex problems. For example, when calculating torque on a coil inside a solenoid, you'd use the magnetic field value calculated earlier to find the torque using \( \tau = n' I_c A B \sin \theta \).
Practicing these problem-solving steps enhances one's ability to approach various physics challenges effectively.

Electromagnetic induction refers to the generation of an electromotive force (EMF) across an electrical conductor when it is exposed to a varying magnetic field. This principle is foundational in many electrical technologies like transformers and generators.
In the problem at hand, a coil within a solenoid experiences a torque due to its orientation and the current it carries. If this solenoid's current and, consequently, its magnetic field were to change with time, it could induce an EMF in the coil, illustrating electromagnetic induction in action.
Transforming energy from a magnetic field into electrical energy forms the basis for devices that utilize electromagnetic induction. Grasping this concept helps in understanding and designing circuits where inductance and magnetic fields play a key role.