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A long straight wire along the Z-axis ca...

A long straight wire along the Z-axis carries a current I in the negative z-direction. The magnetic vector field B at a point having coodinates (x, y) in the z = 0 plane is

A

`(mu_(0)i)/(2pi)((yhati-xhatj))/((x^(2)+y^(2)))`

B

`(mu_(0)i)/(2pi)((xhati+yhatj))/((x^(2)+y^(2)))`

C

`(mu_(0)i)/(2pi)((xhatj-yhati))/((x^(2)+y^(2)))`

D

`(mu_(0)i)/(2pi)((xhatj-yhati))/((x^(2)+y^(2)))`

Text Solution

Verified by Experts

The correct Answer is:
A
Magnetic field at `P` is `barB`, perpendicular to `OP` in the direction shown in figure.
So, `barB=B sin theta hati-/B cos theta hatj`
Here `B=mu_(0)/(2pi)I/r`
`sin theta=y/r` and `cos theta=x/r`
`:.barB=(mu_(0)I)/(2pi)1/r^(2)(yhati-xhatj)=(mu_(0)I(yhati-xhatj))/(2pi(x^(2)+y^(2))`
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