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Magnetic Field due to a Straight Wire

Magnetic field due to a current carrying wire at point P which lies at perpendicular distance r from the wire, as shown in Fig. 15, is given as:
 
81879.png
 
From Fig. 15 81885.png
 
84560.png
Fig. 15
 
and 81894.png
 
Hence, 81900.png

For a wire of finite length

The magnetic field at a point which lies on perpendicular bisector of the finite length wire,
 
φ1 = φ2 = φ So 81906.png
 
82105.png
Fig. 16

For a wire of infinite length

When the linear conductor XY is of infinite length and point P lies near the center of the conductor, φ1 = φ2 = 90o.
 
81912.png 81920.png
 
82114.png
Fig. 17

For a wire of semi-infinite length

When the linear conductor is of infinite length and point P lies near the end Y or X, φ1 = 90° and φ2 = 0°.
 
So, 82120.png82126.png
 
83575.png
Fig. 18

For axial position of wire

When point P lies on the axial position of the current-carrying conductor, then magnetic field at P is given as: B = 0
 
83557.png
Fig. 19




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