A conductor lies along the z-axis at -1.5 ≤ z< 1.5 m and carries a fixed current of 10.An in^-az direction (see figure).
B = 3.0 x 10-4 e-0.2x a_y T, find the power required to move the conductor at constant speed to x = 2.0 , y = 0 in 5 x10^-3 s. Assume parallel motion along the x axis.

1.57 W

2.97 W

04.85 W

29.7 W

Solution

2.97 W

When force exerted on a current carrying conductor
F_ext = BIL
$average space power space equals space fraction numerator Work space done over denominator TIme space taken end fraction straight P space equals 1 over straight t integral subscript 0 superscript 2 straight F subscript ext. end subscript space dx space equals space 1 over straight t integral subscript 0 superscript 2 straight B space left parenthesis straight x right parenthesis IL space dx space equals space fraction numerator 1 over denominator 5 space straight x space 10 to the power of negative 3 end exponent end fraction integral subscript 0 superscript 2 space 3 space straight x space 10 to the power of negative 4 end exponent straight e to the power of negative 0.2 end exponent space straight x space 10 space straight x space space 3 dx space equals space 9 open square brackets 1 minus blank over straight e to the power of 0.4 end exponent close square brackets space equals space 2.967 space almost equal to 2.97 space straight W$

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