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yarga [219]
3 years ago
13

A long solenoid has a diameter of 11.1 cm. When a current i exists in its windings, a uniform magnetic field of magnitude B = 42

.9 mT is produced in its interior. By decreasing i, the field is caused to decrease at the rate of 6.65 mT/s. Calculate the magnitude of the induced electric field (a) 4.34 cm and (b) 7.46 cm from the axis of the solenoid.
Physics
1 answer:
Pepsi [2]3 years ago
6 0

Answer:

E(1) = 1.44\times 10^{-4} v/m

E(2) = 1.34\times 10^{-4} v/m

Explanation:

Given data:

diameter of solenoid is 11.1 cm

B = 42.9 mT

dR = 6.65 mT/s

d(1) = 4.34 cm

d(2) = 7.46 cm

we know that

electric field due to solenoid is given as

E = 1/2 dB/dt (r)

E(1)= \frac{0.0434}{2} \times (6.65\times 10^{-3})

E(1) = 1.44\times 10^{-4} v/m

E = 1/2 dB/dt (R^2)/r

E(2)= \frac{0.055^2}{2\times 0.0746} \times (6.65\times 10^{-3})

E(2) = 1.34\times 10^{-4} v/m

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The sound level at a distance of 1.48 m from a source is 120 dB. At what distance will the sound level be 70.7 dB?
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Answer:

The second distance of the sound from the source is 431.78 m..

Explanation:

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second distance of the sound from the source, r₂ = ?

The intensity of sound in W/m² is given as;

dB = 10 Log[\frac{I}{I_o} ]\\\\For \ 120 dB\\\\120 = 10Log[\frac{I}{1*10^{-12}}]\\\\12 =  Log[\frac{I}{1*10^{-12}}]\\\\10^{12} = \frac{I}{1*10^{-12}}\\\\I = 10^{12} \ \times \ 10^{-12}\\\\I = 1 \ W/m^2

For \ 70.7 dB\\\\70.7 = 10Log[\frac{I}{1*10^{-12}}]\\\\7.07 =  Log[\frac{I}{1*10^{-12}}]\\\\10^{7.07} = \frac{I}{1*10^{-12}}\\\\I = 10^{7.07} \ \times \ 10^{-12}\\\\I = 1 \times \ 10^{-4.93} \ W/m^2

The second distance, r₂, can be determined from sound intensity formula given as;

I = \frac{P}{A}\\\\I = \frac{P}{\pi r^2}\\\\Ir^2 =  \frac{P}{\pi }\\\\I_1r_1^2 = I_2r_2^2\\\\r_2^2 = \frac{I_1r_1^2}{I_2} \\\\r_2 = \sqrt{\frac{I_1r_1^2}{I_2}} \\\\r_2 =   \sqrt{\frac{(1)(1.48^2)}{(1 \times \ 10^{-4.93})}}\\\\r_2 = 431.78 \ m

Therefore, the second distance of the sound from the source is 431.78 m.

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