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Magnetism and Matter
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Magnetic field and it's effect
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S 3 : M a g n e t i c f i e l d o n t h e ax i s o f a c u r re nt c a r r y i n g rWhat you already know What you will learn
➢ Biot-Savart’s law ➢ Magnetic field on the axis of
➢ Magnetic field due to: current carrying ring
▪ A straight current carrying wire ➢ Magnetic field at the centre of
▪ An infinite and semi-infinite wire circular arc
➢ Introduction to solenoid
, MAGNETIC FIELD ON THE AXIS OF A CURRENT CARRYING RING
Magnetic field at point 𝑃 :
𝑌
𝑟Ԧ 𝑑𝐵
𝑖
𝑖
𝜃
𝑃
𝑋
𝑥
𝑅
𝑑𝐵
𝑑𝑙
𝑑𝑙
Front view Side view
, MAGNETIC FIELD ON THE AXIS OF A CURRENT CARRYING RING
Magnetic field at point 𝑃 :
𝑌
Consider a current carrying element 𝑑𝑙 at the top-most point of the 𝑑𝑙 90°
coil. The current in the wire is in the anti-clockwise direction from the
viewpoint of 𝑃. Using ‘Biot-savart law’ and ‘Right hand thumb rule’, we 𝑟Ԧ
can say that direction of the magnetic field at point 𝑃 on the axis of 𝑖 𝑅
the coil due to this element will be in slanted upward direction, as 𝜃
shown by the pink arrow in the adjacent figure.
𝑃
Similarly, choose a mirror current carrying element 𝑑𝑙 at the bottom
most point of the coil. Using ‘Biot-savart law’ and ‘Right hand thumb 𝑥
rule’, we can say that direction of the magnetic field at point 𝑃 on the 𝑑𝑙
axis of the coil due to this element will be in slanted downward
direction, as shown by the blue arrow in the adjacent figure.
The magnetic field vectors due to the element will be,
𝜇0 𝑖(𝑑𝑙 × 𝑟)Ԧ
𝑑𝐵 =
4𝜋 𝑟Ԧ 3
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