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daser333 [38]
3 years ago
7

If 62.9 cm of copper wire (diameter = 1.15 mm, resistivity = 1.69 × 10-8Ω·m) is formed into a circular loop and placed perpendic

ular to a uniform magnetic field that is increasing at the constant rate of 8.43 mT/s, at what rate is thermal energy generated in the loop?
Physics
1 answer:
deff fn [24]3 years ago
8 0

Answer:

The answer is "\bold{7.30 \times 10^{-6}}"

Explanation:

length of the copper wire:

L= 62.9 cm

r is the radius of the loop then:

r=\frac{L}{2 \pi}\\

  =\frac{62.9}{2\times 3.14}\\\\=\frac{62.9}{6.28}\\\\=10.01\\

area of the loop Is:

A_L= \pi r^2

     =100.2001\times 3.14\\\\=314.628

change in magnetic field is:

=\frac{dB}{dt} \\\\ = 0.01\ \frac{T}{s}

then the induced emf is:  e = A_L \times \frac{dB}{dt}

                                              =314.628 \times 0.01\\\\=3.14\times 10^{-5}V

resistivity of the copper wire is: \rho =  1.69 × 10-8Ω·m

diameter d = 1.15mm

radius (r) = 0.5mm

               = 0.5 \times 10^{-3} \ m

hence the resistance of the wire is:

R=\frac{\rho L}{\pi r^2}\\

   =\frac{1.69 \times 10^{-8}(62.9)}{3.14 \times (0.5 \times 10^{-3})^2}\\\\=\frac{1.69 \times 10^{-8}(62.9)}{3.14 \times 0.5 \times 0.5 \times 10^{-6}}\\\\=\frac{1.69 \times 10^{-8}(62.9)}{3.14 \times 0.25 \times 10^{-6}}\\\\=135.41 \times 10^{-2}\\=1.35\times 10^{-4}\\

Power:

P=\frac{e^2}{R}

=\frac{3.14\times 10^{-5}\times 3.14\times 10^{-5}}{1.35 \times 10^{-4}}\\\\=7.30 \times 10^{-6}

The final answer is: \boxed{7.30 \times 10^{-6} \ W}

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  Here we are asked to calculate the the distance of Saturn from sun.It can solved by comparing it with earth.

Let the distance from sun and orbital period of Saturn is denoted as R_{1} and T_{1} respectively.

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Hence distance of Saturn from sun  is calculated as -

From Kepler's law as mentioned above-

                                    R_{1} ^{3} =R_{2} ^{3} *\frac{T_{1} ^{2} }{T_{2} ^{2} }

                                             =[1 ]^{3} *\frac{[29.46]^{2} }{[1]^{2} } AU

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                                        ⇒R_{1} =\sqrt[3]{867.8916}

                                           =9.5386 AU [ans]

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