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galben [10]
3 years ago
6

Two long, parallel wires carry unequal currents in the same direction. The ratio of the currents is 3 to 1. The magnitude of the

magnetic field at a point in the plane of the wires and 10 cm from each wire is 4.0 μT. What is the larger of the two currents?
Physics
1 answer:
astraxan [27]3 years ago
3 0

Answer:

3A is the larger of the two currents.

Explanation:

Let the currents in the two wires be I₁ and I₂

given:

Magnitude of the electric field, B = 4.0μT = 4.0×10⁻⁶T

Distance, R = 10cm = 0.1m

Ratio of the current = I₁ : I₂ = 3 : 1

Now, the magnitude of a magnetic field at a distance 'R' due to the current 'I' is given as

B = \frac{\mu_oI}{2\pi R}

Where \mu_o is the magnitude constant = 4π×10⁻⁷ H/m

Thus, the magnitude of a magnetic field due to I₁ will be

B_1 = \frac{\mu_oI_1}{2\pi R}

B_2 = \frac{\mu_oI_2}{2\pi R}

given,

B = B₁ - B₂ (since both the currents are in the same direction and parallel)

substituting the values of B, B₁ and B₂

we get

4.0×10⁻⁶T =  \frac{\mu_oI_1}{2\pi R} - \frac{\mu_oI_2}{2\pi R}

or

4.0×10⁻⁶T =  \frac{\mu_o}{2\pi R}\times (I_1-I_2 )

also

\frac{I_1}{I_2} = \frac{3}{1}

⇒I_1 = 3\times I_2

substituting the values in the above equation we get

4.0×10⁻⁶T =  \frac{4\pi\times 10^{-7}}{2\pi 0.1}\times (3 I_2-I_2)

⇒I_2 = 1A

also

I_1 = 3\times I_2

⇒I_1 = 3\times 1A

⇒I_1 = 3A

Hence, the larger of the two currents is 3A

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Answer:

The distance it has traveled is 3,050 m and the magnitude of its displacement is 650 m north.

Explanation:

Distance refers to the length between any two points in space, while displacement refers to the distance from a start position to an end position regardless of the path.

In other words, distance refers to how much space an object travels during its movement; is the quantity moved. It is also said to be the sum of the distances traveled. The distance traveled by a mobile is the length of its trajectory and it is a scalar quantity. In this case, the distance is calculated as:

1850 m + 1200 m= 3,050 m

Displacement refers to the distance and direction of the final position from the initial position of an object. The displacement effected is a vector quantity. The vector representing the displacement has its origin in the initial position, its end in the final position, and its module is the distance in a straight line between the initial and final positions. That is, when expressing the displacement it is done in terms of the magnitude with its respective unit of measurement and the direction because the displacement is a vector type quantity. Mathematically, the displacement (Δd) is calculated as:

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In this case, the displacement is calculated as:

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<u><em>The distance it has traveled is 3,050 m and the magnitude of its displacement is 650 m north.</em></u>

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