An infinite long straight wire with current I flowing along the positve z-axis is located at coordinates `P(-12m, 5m)`. Determine the unit vector showing the direction of magnetic field at the origin.

Options

A. `1/13(12hati+5hatj)`
B. `1/13(5hati+12hatj)`
C. `1/13(5hati-12hatj)`
D. `1/13(-5hati+12hatj)`

Answer

B

Explanation

Unit vector of `hat(u)_b`
`hatu_b=haticos(90- theta)+hatjcos theta= sin thetahati+cos theta hatj`

`sin theta=5/(sqrt(5^2+12^2))=5/13, cos theta=12/(sqrt(5^2+12^2))=12/13`
`hatu_B=5/13 hati+12/13hatj=1/13(5hati+12hatj)`