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. 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`