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A conductor lies along the z-axis at -...

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`.

A

1.57 W

B

2.97 W

C

14.85 W

D

29.7 W

Text Solution

Verified by Experts

The correct Answer is:
B
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`
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