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Alex787 [66]
3 years ago
5

Two long straight wires are parallel and carry current in the same direction. The currents are 8.0 and 12 A and the wires are se

parated by 0.40 cm. The magnetic field at a point midway between the wires is:_______a. 0b. 4 x 10^-4c. 8 x 10^-4d. 12 x 10^-4e. 20 x 10^-4
Physics
1 answer:
Bess [88]3 years ago
8 0

A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any point is specified by two values, the direction and the magnitude; such that it is a vector field. Mathematically it is described as,

B = \frac{\mu_0 I}{2\pi d}

Here

\mu_0=  Permeability at free space constant

I_{1,2}= Current at each object

d = Distance to the center point of the two object

Two magnetic field due to the current in the same directions then is,

B = \frac{\mu_0 I_1}{2\pi d_1}+\frac{\mu_0 I_2}{2\pi d_2}

Replacing,

B = \frac{(4\pi *10^{-7})(8)}{2\pi (2*10^{-3})}+\frac{(4\pi *10^{-7})(12)}{2\pi (2*10^{-3})}

B = 8*10^{-4} +12*10^{-4}

B = 20*10^{-4}T

Therefore the correct answer is E.

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Suppose that 4.4 moles of a monatomic ideal gas (atomic mass = 7.9 × 10-27 kg) are heated from 300 K to 500 K at a constant volu
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Answer:

1) ΔQ₁ = 10.97 x 10³ J = 10.97 KJ

2) W₁ = 0 J

3) P = 41.66 x 10³ Pa = 41.66 KPa

4) v = 1618.72 m/s

5) ΔQ₂ = - 18.29 x 10³ J = - 18.29 KJ

6) W₂ = - 7.33 KJ

Explanation:

1)

The heat transfer for a constant volume process is given by the formula:

ΔQ₁ = ΔU = n Cv ΔT

where,

ΔQ₁ = Heat transfer during constant volume process

ΔU = Change in internal energy of gas

n = No. of moles = 4.4 mol

Cv = Molar Specific Heat at Constant Volume = 12.47 J/mol.k

ΔT = Change in Temperature = T₂ - T₁ = 500 k - 300 k = 200 k

Therefore,

ΔQ₁ = (4.4 mol)(12.47 J/mol.k)(200 k)

<u>ΔQ₁ = 10.97 x 10³ J = 10.97 KJ</u>

<u></u>

2)

Since, work done by gas is given as:

W₁ = PΔV

where,

ΔV = 0, due to constant volume

Therefore,

<u>W₁ = 0 J</u>

<u></u>

4)

The average kinetic energy of a gas molecule is given as:

K.E = (3/2)KT

but, K.E is also given by:

K.E = (1/2)mv²

Comparing both equations:

(1/2)mv² = (3/2)KT

mv² = 3KT

v = √(3KT/m)

where,

v = average speed of gas molecue = ?

K = Boltzman Constant = 1.38 x 10⁻²³ J/k

T = Absolute Temperature = 500 K

m = mass of a molecule = 7.9 x 10⁻²⁷ kg

Therefore,

v = √[(3)(1.38 x 10⁻²³ J/k)(500 k)/(7.9 x 10⁻²⁷ kg)]

<u>v = 1618.72 m/s</u>

<u></u>

3)

From kinetic molecular theory, we know that or an ideal gas:

P = (1/3)ρv²

where,

P = pressure of gas = ?

m = Mass of Gas = (Atomic Mass)(No. of Atoms)

m = (Atomic Mass)(Avogadro's Number)(No. of Moles)

m = (7.9 x 10⁻²⁷ kg/atom)(6.022 x 10²³ atoms/mol)(4.4 mol)

m = 0.021 kg

ρ = density = mass/volume = 0.021 kg/0.44 m³ = 0.0477 kg/m³

Therefore,

P = (1/3)(0.0477 kg/m³)(1618.72 m/s)²

<u>P = 41.66 x 10³ Pa = 41.66 KPa</u>

<u></u>

5)

The heat transfer for a constant pressure process is given by the formula:

ΔQ₂ =  n Cp ΔT

where,

ΔQ₂ = Heat transfer during constant pressure process

n = No. of moles = 4.4 mol

Cp = Molar Specific Heat at Constant Pressure = 20.79 J/mol.k

ΔT = Change in Temperature = T₂ - T₁ = 300 k - 500 k = -200 k

Therefore,

ΔQ₂ = (4.4 mol)(20.79 J/mol.k)(-200 k)

<u>ΔQ₂ = - 18.29 x 10³ J = - 18.29 KJ</u>

<u>Negative sign shows heat flows from system to surrounding.</u>

<u></u>

6)

From Charles' Law, we know that:

V₁/T₁ = V₂/T₂

V₂ = (V₁)(T₂)/(T₁)

where,

V₁ = 0.44 m³

V₂ = ?

T₁ = 500 K

T₂ = 300 k

Therefore,

V₂ = (0.44 m³)(300 k)/(500 k)

V₂ = 0.264 m³

Therefore,

ΔV = V₂ - V₁ = 0.264 m³ - 0.44 m³ = - 0.176 m³

Hence, the work done , will be:

W₂ = PΔV = (41.66 KPa)(- 0.176 m³)

<u>W₂ = - 7.33 KJ</u>

<u>Negative sign shows that the work is done by the gas</u>

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