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

Answer

B

Explanation

`F_("net") = B (x) IL`
`P = (1)/(t) int_(0)^(2) F_("ext") dx = (1)/(t) int_(0)^(2) B(x) IL dx`
= `(1)/(5 xx 10^(-3)) int_(0)^(2) 3 xx 10^(-4) e^(-0.2x) xx 10 xx 3dx = 9 (1- e^(-0.4))`
`= 9 [ 1- (1)/(e^(0.4))] = 2.96`