A conductor lies along the ` z`-axis at ` -1.5 le z lt 1.5 m` and carries a fixed current of `10.0 A` in `- hat(a)_(z)` direction ( see figure). For a field `vec(B) = 3.0 xx 10^(-4) e^(-0.2x) hat(a)_(y) T`, find the power required to move the conductor at constant speed to `x = 2.0 m , y = 0 m ` in `5xx 10^(-3)s` . Assume parallel motion along the ` x-axis`.

Options

A. `14*85W`
B. `29*7W`
C. `1*57W`
D. `2*97W`

Answer

D

Explanation

Here, `l=1*5+1*5=3*0m, I=10*0A`,
Average Power=work/time

`W=int_(0)^(2)Fdx=int_(0)^(2) BIldx`
`=int_(0)^(2)3*0xx10^-4e^(-0*2x)xx10xx3dx`
`=9xx10^-3xx int_(0)^(2)e^(-0*2x)dx`
`=9xx10^-3[(e^(-0*2x))/(-0*2)]_0^2=9xx10^-3[(e^(-0*2xx2)-1)/(-0*2)]`
`=(9xx10^-3)/(0*2)xx[1-e^(-0*4)]=(9xx10^-3)/(0*2)xx0*33`
`=(2*97xx10^-3)/(0*2)J`
`P=(2*97xx10^-3)/((0*2)xx5xx10^-3)=2*97W`