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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
Work done in moving the conductor is ,
`W = int_(0)^(2) Fdx`
`= int_(0)^(2) 3.0 xx 10^(-4) e^(-0.2x) xx 10xx 3dx`
` = 9 xx 10^(-3) int _(0)^(2) e^( -0.2x) dx` ` = ( 9 xx 10^(-3))/(0.2) [ -e^( 0.2 xx2) + 1 ] B = 3.0 xx10^(-4) e^(-0.2x)`
( By exponential function )
`= ( 9 xx 10^(-3))/(0.2) xx [ 1- e^(-0.4)]`
` = 9 xx 10^(-3) xx (0.33) = 2.97 xx 10^(-3)J`
`P = ( W) /(t)`
`p = (2.97 xx 10^(-3))/((0.2) xx 5 xx 10^(-3)) = 2.97 W`
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