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

B

Explanation

Force exerted on a current carrying conductor `F_("ext")=B(x)IL`
Averate power `=("Work done")/("Time taken") , P=1/t int_(0)^(2)F_("ext").dx=-1/tint_(0)^(2)B(x)ILdx`
`=1/(5xx10^(-3))int_(0)^(2)3xx10^(-04)e^(-0.2x)xx10xx3dx, =9[1-e^(-0.4)]=9[1-1/(e^(0.4))]=2.967~~2.97W`