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

Question

A long straight wire along z axis carries a current I in the negative z direction. The magnetic vector B at a point having coordinates (x, y) in the z = 0 plane is (A) (μ0I/2π) ((yi-xj)/(x2-y2)) (B) (μ0I/2π) ((x hati+y hatj)/(x2+y2)) (C) (μ0I/2π) ((xi-yj)/(x2+y2)) (D) (μ0I/2π) (x hati+y hatj/x2+y2)

Tardigrade Admin · Accepted Answer

Here, current flows in the long straight wire along -ve z direction. So magnetic field B lies in (x, y) plane

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

$\frac{μ _{0} I}{2 π}$ $\frac{( y _{i} - x _{j} )}{( x ^{2} - y ^{2} )}$

$\frac{μ _{0} I}{2 π}$ $\frac{( x i ^ + y j ^ )}{( x ^{2} + y ^{2} )}$

$\frac{μ _{0} I}{2 π}$ $\frac{( x _{i} - y _{j} )}{( x ^{2} + y ^{2} )}$

$\frac{μ _{0} I}{2 π}$ ${\frac{x i ^ + y j ^}{x ^{2} + y ^{2}}}$

Here, current flows in the long straight wire along $- v e z$ direction. So magnetic field B lies in $(x, y)$ plane

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

2πμ0​I​(x2−y2)(yi​−xj​)​

2πμ0​I​(x2+y2)(xi^+yj^​)​

2πμ0​I​(x2+y2)(xi​−yj​)​

2πμ0​I​{x2+y2xi^+yj^​​}