A conducting wire bent in the form of a parabola `y^2=2x`, carries a current `I=2A` as shown in figure. The wire is subjected to a uniform magnetic field `vecB=-2hatk` tesla. The magnetic force on the wire in (newton) is

Options

A. `-8hati`
B. `-16hati`
C. `8hati`
D. `16hati`

Explanation

When `x=2m`,
`y^2=2xx2=4` or `y=2m`
`:.` length `AB=2+2=4m`
This bent conducting wire will be of vector length
`vecl=vec(AB)=4(-hatj)=-4hatj`
Force on wire, `vecF=IveclxxvecB`
`=2[(-4hatj)xx(-2hatk)]=16hati`