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. 4.45 W
D. 9.87 W

Answer

B

Explanation

Force exerted on curretn carrying conductor (F)=BII
Given ,`B =3xx10^(4)e^(0.2x)ay,I=10.0 A`
`Average power=(Work done)/(Time taken)`
`P=(1)/(5xx10^(-3)intoverset(2)underset(0)int3xx10^(-4)e^(-0.2x)xx10xx3dx`
`=9[1-e^(-0.4)]=9[1-(1)/(e^(0.4))]=2.967 W=2.97 W`