Axis of a solid cylinder of infinite length and radius R lies along y-axis. It carries a uniformly distributed current I along +y direction. Magnetic field at a point `(R//2, y, R//2)` is

Options

A. `(mu_(0)I)/(4piR)(hati-hatk)`
B. `(mu_(0)I)/(2piR)(hatj-hati)`
C. `(mu_(0)I)/(4piR)hatj`
D. `(mu_(0)I)/(4piR)(hatj+hati)`

Answer

A

Explanation

`r=Rsqrt(2), B=(mu_(0)I(R//sqrt(2)))/(2piR^(2))=(mu_(0)I)/(2sqrt(2)piR)`

`vec(B)=B[cos45^(@)hati+sin45^(@)(-hatk)]=(mu_(0)I)/(4piR)[hati-hatk]`