A conductor lies along the z-axis at `-1.5 le z le 1.5` m and carries a fixed current of `1.0 A` in `-hata_(z)` direction (see figure). For a field `vec(B) = 3.0 xx 10^(-4) e^(-0.2 x) hata_(y)` T, find the power required to move the conductor at constant speed to `x = 2.0 m , y = m` in `5 xx 10^(-3)s`. Assume parallel motion along the x-axis.

Options

A. `1.57 W`
B. `2.97 W`
C. `14.85 W`
D. `29.7 W`

Answer

2

Explanation

`F_(ext)=B(x)IL`
`P=1/tunderset(0)overset(2)intF_(ext)dx=1/tunderset(0)overset(2)intB(x)ILdx=1/(5xx10^(-3))underset(0)overset(2)int3xx10^(-4)e^(-0.2x)xx10xx3dx`
`=9[1-1/e^(0.4)]=2.96`