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The force per unit length of two conductors carrying equal currents of 5A separated by a distance of 20cm in air(in 10-6 order)
- a)25
- b)35
- c)40
- d)50
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
The force per unit length of two conductors carrying equal currents of...
Answer: a
Explanation: The force per unit length of two conductors is given by
F = μ I1xI2/2πD, where I1 = I2 = 5 and D = 0.2. Thus F = 4π x 10-7 x 52/ 2π x 0.2 = 25 x 10-6 units.
Explanation: The force per unit length of two conductors is given by
F = μ I1xI2/2πD, where I1 = I2 = 5 and D = 0.2. Thus F = 4π x 10-7 x 52/ 2π x 0.2 = 25 x 10-6 units.
Most Upvoted Answer
The force per unit length of two conductors carrying equal currents of...
Force per unit length between two conductors carrying equal currents can be calculated using the formula:
\[ F = \frac{{\mu_0 \cdot I_1 \cdot I_2 \cdot l}}{{2 \pi \cdot d}} \]
where:
\( F \) = force per unit length
\( \mu_0 \) = permeability of free space (\( 4\pi \times 10^{-7} \, \text{N/A}^2 \))
\( I_1 \) and \( I_2 \) = currents in the two conductors (\( 5 \, \text{A} \) each)
\( l \) = length of the conductors (\( 20 \, \text{cm} = 0.2 \, \text{m} \))
\( d \) = distance between the conductors (\( 20 \, \text{cm} = 0.2 \, \text{m} \))
Let's substitute the given values into the formula:
\[ F = \frac{{4\pi \times 10^{-7} \cdot 5 \cdot 5 \cdot 0.2}}{{2\pi \cdot 0.2}} \]
Simplifying the equation:
\[ F = 25 \times 10^{-6} \, \text{N/m} \]
Therefore, the force per unit length between the two conductors is \( 25 \, \text{N/m} \), which is equivalent to \( 25 \times 10^{-6} \, \text{N/}\mu\text{m} \).
Hence, the correct answer is option 'A' (25).
\[ F = \frac{{\mu_0 \cdot I_1 \cdot I_2 \cdot l}}{{2 \pi \cdot d}} \]
where:
\( F \) = force per unit length
\( \mu_0 \) = permeability of free space (\( 4\pi \times 10^{-7} \, \text{N/A}^2 \))
\( I_1 \) and \( I_2 \) = currents in the two conductors (\( 5 \, \text{A} \) each)
\( l \) = length of the conductors (\( 20 \, \text{cm} = 0.2 \, \text{m} \))
\( d \) = distance between the conductors (\( 20 \, \text{cm} = 0.2 \, \text{m} \))
Let's substitute the given values into the formula:
\[ F = \frac{{4\pi \times 10^{-7} \cdot 5 \cdot 5 \cdot 0.2}}{{2\pi \cdot 0.2}} \]
Simplifying the equation:
\[ F = 25 \times 10^{-6} \, \text{N/m} \]
Therefore, the force per unit length between the two conductors is \( 25 \, \text{N/m} \), which is equivalent to \( 25 \times 10^{-6} \, \text{N/}\mu\text{m} \).
Hence, the correct answer is option 'A' (25).
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