Thus the integral of the upper side of the figure that represents one is equal to an integral part of side two that is moving downwards. We have shown above that the field is pointing upwards inside the solenoid, hence the horizontal portions of loop c do not contribute anything to the integral. It happens since it encloses no electrical currents. By Ampère's law, we can say that the line integral of B that is the magnetic flux density vector around this loop is zero. Now consider the imaginary loop ‘c’ from the figure, it is located inside the solenoid.

Since we are dealing with a long solenoid, due to symmetry all of the components of the magnetic field that are not pointing upwards may cancel out. If we wrap our right hand around a wire by pointing the thumb in the direction of the current, the curl of the fingers represents how the field behaves.

We can confirm this by applying the right-hand grip rule or right-hand thumb rule for the field that is present around a wire. We immediately know that from the figure, the flux density of the vector points is in the positive z-direction inside the solenoid, and outside the solenoid, it is in the negative z-direction. The derivation of the magnetic flux density surrounding a solenoid is long enough so that fringe effects can be ignored. The magnetic field inside an infinitely long solenoid is homogeneous and its strength neither depends on the distance from the axis nor the solenoid's cross-sectional area. Or 12.57 x 10 − ⁷ Hm, N is a number of turns, I is the current flowing through the solenoid, and l is the length of the solenoid. Μ 0 is the magnetic constant whose value is 4π x 10 - ⁷ Hm Here B represents the magnetic flux density, Hence magnetic field formula of the solenoid equation is given as follows: The helical coil of a solenoid does not necessarily need to revolve around a straight-line axis, for example, William Sturgeon's electromagnet of 1824 consisted of a solenoid bent in the form of horseshoe shape. According to the study of electromagnetism, a solenoid is a coil whose length is greater than its diameter this means that it is rod-shaped. The coil can be arranged to produce a uniform magnetic field in a volume of space when an electric current is passed through it. It is a type of electromagnet, its purpose is to generate a controlled magnetic field through a coil that is wound into a tightly packed helix. The term solenoid in Greek means 'pipe-shaped'.

Magnetic flux solenoid formula