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solenoid magnetic field details

Magnetic field is a vector quantity {vector B}, therefore, it has two components to represent it: Magnitude {B}, and
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-
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:
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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Solution Preview

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.