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    solenoid magnetic field details

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    Magnetic field is a vector quantity {vector B}, therefore, it has two components to represent it: Magnitude {B}, and
    direction.
    To find the direction, Right Hand Thumb Rule is used, while for magnitude, a basic law of Biot-Savart Law is used.
    Right Hand Thumb Rule [RHTR} states {in my words} that
    - if you are given a current {I} carrying conductor, a magnetic field {B} is produced around it.
    - The magnetic field lines are in concentric circles, in plane perpendicular to the direction of current.
    -It you told your right hand four fingers, and keep your thumb straight. If the current is in the direction of thumb,
    then magnetic field (due to the current} lines will be along the direction of fingers.
    NOTE: The direction of magnetic field direction is represented by field or force lines.
    NOTE: denser the field lines {i.e., large number of field lines concentrated some where) == strong field; and vice-
    a-versa.
    This concept is applicable in the case of solenoid, you have shown and have asked for. To explain you, I have
    attached my camera pictures. May be the quality of the picture not so good, but please bear with me.
    ln the attachments, I have started with RHTR:
    Because,
    Solenoid {picture you have shown in attachment): N number of loops, side-by-side == conductors in shape of
    loop, parallel to one another.
    Page 1
    -First: Single conductor and field around it [in a plane perpendicular to the direction of current)
    -lf no. of conductors are placed sided-by-side, the field lines will be combination of all of them [see Attachment �"
    combined field lines are darkened)
    Page 2
    -Now take an example of rectangularrsquare loop, combined filed of four sides - four conductors. Inside the loop,
    field will be in the same direction {for each apply RHTR). Outside the loop, field direction will be opposite to that of
    inside field. Outside, each side of the loop, field will be dominated by a conductor closer to it. Though, inside, field
    is combined of all sides. Obviously, inside the field will be stronger than outside.
    -Now replace square loop with circular loop == Very large number of conductors side by side, with a small
    deviation of angle with respecto one another. But concept of loop will be applied, except instead of 4 conductors,
    very large number of conductors.
    -Once single loop is done, now extend further: N number of loops side by side == N conductors side~by-side,
    each in shape of a loop. Now you see the combined field lines profile [see attachment}

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    https://brainmass.com/physics/electricity-magnetism/solenoid-magnetic-field-details-540483

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    1
    To derive the magnetic field due to a solenoid, concept of magnetic field
    due to coil is utilized: Magnetic field on the axis ...

    Solution Summary

    Magnetic field due to current carrying solenoid is derived.

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