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The force between two parallel conductors, each of length $50 \mathrm{m}$ and distant $20 \mathrm{cm}$ apart, is 1 N. If the current in one conductor is double than that in another one, then their values will respectively be:
(A) 100 A and 200 A
(B) 50 A and 400 A
(C) 10 A and 30 A
(D) 5 A and 25 A

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Last updated date: 13th Jun 2024
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Answer
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Hint We know that conductors are the materials or substances which allow electricity to flow through them. They conduct electricity because they allow electrons to flow easily inside them from atom to atom. Also, conductors allow the transmission of heat or light from one source to another.Examples of conductors include metals, aqueous solutions of salts (i.e., ionic compounds dissolved in water), graphite, and the human body. Examples of insulators include plastics, Styrofoam, paper, rubber, glass and dry air. The most electrically conductive element is silver, followed by copper and gold. Silver also has the highest thermal conductivity of any element and the highest light reflectance.

Complete step by step answer
It is given that,
$\mathrm{F}=1 \mathrm{N}, \mathrm{l}=50 \mathrm{m}, \mathrm{r}=20 \mathrm{cm}=0.2 \mathrm{m}, \mathrm{i}_{2}=2 \mathrm{i}_{1}$
The force between two long parallel conductors separated by
distance $r$, is
$\mathrm{F}=\dfrac{\mu_{0}\left(\mathrm{i}_{1}\right)\left(\mathrm{i}_{2}\right) \mathrm{l}}{2 \pi \mathrm{r}}$
After we put the values, we get that:
$\mathrm{F}=\dfrac{\left(4 \pi \times 10^{-7}\right)\left(\mathrm{i}_{1}\right)\left(2 \mathrm{i}_{1}\right) 50}{2 \pi 0.2}$
$\mathrm{i}_{1}^{2}=\dfrac{2 \pi(0.2)}{\left(8 \pi \times 10^{-7}\right) 50}$
After the evaluation we get that:
$\mathrm{i}_{1}^{2}=\dfrac{0.2}{\left(200 \times 10^{-7}\right)}$
$\mathrm{i}_{1}^{2}=10000$
$\mathrm{i}_{1}=100 \mathrm{A}$
and $\mathrm{i}_{2}=2 \mathrm{i}_{1}=200 \mathrm{A}$

Hence the correct option is option A.

Note: We can say that conduction is the process by which heat energy is transmitted through collisions between neighboring atoms or molecules. Conduction occurs more readily in solids and liquids, where the particles are closer to together, than in gases, where particles are further apart. During the day, sunlight heats the ground, which in turn heats the air directly above it via conduction. At night, the ground cools and the heat flows from the warmer air directly above to the cooler ground via conduction. The transmission or conveying of something through a medium or passage, especially the transmission of electric charge or heat through a conducting medium without perceptible motion of the medium itself.
The electrons in a piece of metal can leave their atoms and move about in the metal as free electrons. This kinetic energy is transferred from hot parts of the metal to cooler parts by the free electrons. These move through the structure of the metal, colliding with ions as they go.