A semi circular current carrying wire having radius `R` is placed in `x-y` plane with its centre at origin `O` There is non-unifrom magnetic field
`oversetrarrB = (B_(0)x)/(2R) hatk` (here `B_(0)` is +ve contant) is existing in the region The magnetic force acting on semi circular wire will be along
.

Options

A. `-x` - axis
B. `+y` -axis
C. `-y` -axis
D. `+x`- axis

Answer

A

Explanation

`B={(|(B_(0)x)/(2R)|hatk, "when" ,xgt0),(|(B_(0)x)/(2R)|(-hatk),"when",xlt0):}`

`F_("net")=F_(x)hati+F_(Y)hatj`
`F_(y)=sumdF_(y)=0` (from figure)
`F_(x)=sumdF_(x)=-2 int_(0)^(pi//2)dFcos theta` (from figure)
Hence `F_("net")` is along negative x-axis