Question

A conductor lies along the Z-axis at −1.5 ≤ Z ≤ 1.5 m and carries a fixed current of 10.0 A in −a_z​ direction as (see figure). For a field B = 3.0 × 10⁻⁴`"e"^(−0.2"x")`a_y ​T, find the power required to move the conductor at constant speed to x = 2.0 m, y = 0 in 5 × 10⁻³ s. Assume parallel motion along the x-axis.

Options

• 1.57 W

• 2.97 W

• 14.85 W

• 29.7 W

Answer 1

2.97 W

Explanation:

Force exerted on current carrying conductor (F) = BIl

Given, B = 3.0 × 10⁻⁴`"e"^(−0.2"x")`a_y  I = 10.0 A​

Average power = `"Work done"/"Time taken"`

P = `1/"t"int_0^2"F"."d"x=1/"t"int_0^2"B"(x)"IL"."d"x`

P = `1/(5xx10^-3)int_0^2 3xx10^-4"e"^(-0.2x)xx10xx3"d"x` 

= 9`[1-"e"^-0.4]`

= 9 `[1-1/"e"^0.4]`

= 2.967 W = 2.97 W