Mathematical Modeling and Teaching of Outer Magnetic Field of a Solenoid Using Smartphones

The outer magnetic field of a solenoid is commonly ignored and misinterpreted assuming that it is effectively nothing, however in reality, it assuredly exists, nevertheless, reasonably challenging to resolve and teach. Therefore, this work suggests a mathematical modeling approach for determining and teaching the outer magnetic field of a solenoid based on Biot–Savart’s law. The mathematical modeling is managed by using a smartphone embedded with an appropriate magnetic field sensor and application tool. During the performance, the solenoid’s magnetic field is basically varied by changing the current flowing through and the magnetic field is measured by means of smartphone for various distances. The theoretical resolution of the outer magnetic field is also tackled based on the Biot–Savart’s law which leads to a challenging and unknown integral. This approach provides accessibility for physics, teachers and educators to teach and internalize the outer magnetic field of a solenoid and relating Biot–Savart law in a better manner.