BITSAT 2015 Paper

The wire carries a current I in the negative z-direction. We have to consider the magnetic vector field

→

B

at (x, y) in the z = 0 plane.

Magnetic field

→

B

is perpendicular to OP.
∴

→

B

= b sin θ

^

i

- B cos θ

^

j

sin θ =

y

r

, cos θ =

x

r

, B =

µ0I

2πr

∴

→

B

=

µ0I

2πr2

(y

^

i

−x

^

j

)
or

→

B

=

µ0I(y ^ i −x ^ j )

2π(x2+y2)