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3 years ago

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Two rigid rods are oriented parallel to each other and to the ground. The rods carry the same current in the same direction. The

length of each rod is 0.85 m, and the mass of each is 0.073 kg. One rod is held in place above the ground, while the other floats beneath it at a distance of 8.2 × 10−3 m. Determine the current in the rods.

1 answer:

bazaltina [42]3 years ago

5 0

Answer:

The current in the rods is 171.26 A.

Explanation:

Given that,

Length of rod = 0.85 m

Mass of rod = 0.073 kg

Distance $d = 8.2\times10^{-3}\ m$

The rods carry the same current in the same direction.

We need to calculate the current

I is the current through each of the wires then the force per unit length on each of them is

Using formula of force

$\dfrac{F}{L}=\dfrac{\mu_{0}I^2}{2\pi d}$

$\dfrac{mg}{L}=\dfrac{\mu_{0}I^2}{2\pi d}$

Where, m = mass of rod

l = length of rod

Put the value into the formula

$I^2=\dfrac{mgd}{\mu L}$

$I^2=\dfrac{0.073\times9.8\times8.2\times10^{-3}}{2\times10^{-7}}$

$I=\sqrt{29331.4}$

$I=171.26\ A$

Hence, The current in the rods is 171.26 A.

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Explanation:

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$\tan\beta=\frac{8}{4}$

$\beta=63.43^{\circ}$

Now the distance swam by the swimmer in this direction be d.

so,

$d.\cos\beta=w$

$d\times \cos\ 63.43=500$

$d=1118.034\ ft$

Now the distance swept downward:

$\Delta s=\sqrt{d^2-w^2}$

$\Delta s=\sqrt{1118.034^2-500^2}$

$\Delta s=1000\ ft$

2)

On swimming 37° upstream:

<u>The velocity component of stream cancelled by the swimmer:</u>

$v'=v.\cos37$

$v'=4\times \cos37$

$v'=3.1945\ ft.s^{-1}$

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$v_n=v_s-v'$

$v_n=8-3.1945$

$v_n=4.8055\ ft.s^{-1}$

<u>The component of swimmer's velocity heading directly towards the opposite bank:</u>

$v'_r=v.\sin37$

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<u>Now the angle of the resultant velocity of the swimmer from the normal to the stream</u>:

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$\Delta s'=998.11\ ft.s^{-1}$

3)

Time taken in crossing the rive in case 1:

$t=\frac{d}{v_r}$

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$t\approx125\ s$

Time taken in crossing the rive in case 2:

$t'=\frac{d'}{v'_r}$

$t'=\frac{1116.344}{2.4073}$

$t'\approx463.733\ s$

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