MHT CET · Physics · Magnetic Effects of Current
Two thin long parallel wires of same material are separated by a distance ' \(r\) ' Both carry same current ' \(I\) ' in the direction. Hence they will ( \(\mu_0=\) permeability of free space.)
- A Attract each other with a force \(\mu_0 I^{2 / 2 r}\) per unit length
- B Repel each other with a force \(\mu_0 I^2 /(2 \pi r)\) per unit length
- C Attract each other with a force \(\mu_0 I^2 /(2 \pi r)\) per unit length.
- D Repel each other with a force \(\mu_0 I^2 /(2 r)\) per unit length
Answer & Solution
Correct Answer
(C) Attract each other with a force \(\mu_0 I^2 /(2 \pi r)\) per unit length.
Step-by-step Solution
Detailed explanation
The force per unit length between two long current carrying carrying conductors is \(\mathrm{F}=\frac{\mu_0 \mathrm{i}_1 \mathrm{i}_2}{2 \pi \mathrm{r}}\)
where \(\mathrm{d}\) is the distance between the conductors and \(\mathrm{i}_1\) and \(\mathrm{i}_2\) are the currents carried by the conductors.
The conductors attract each other if \(i_1\) and \(i_2\) are in the same direction. Magnetic field created by conductor 1 at the location of the conductor 2 and conductor 2 gets attracted towards conductor 1.
Since \(\mathrm{i}_1=\mathrm{i}_2=\mathrm{i}\)
\(\therefore \mathrm{F}=\frac{\mu_0 \mathrm{i}^2}{2 \pi \mathrm{r}}\)
where \(\mathrm{d}\) is the distance between the conductors and \(\mathrm{i}_1\) and \(\mathrm{i}_2\) are the currents carried by the conductors.
The conductors attract each other if \(i_1\) and \(i_2\) are in the same direction. Magnetic field created by conductor 1 at the location of the conductor 2 and conductor 2 gets attracted towards conductor 1.
Since \(\mathrm{i}_1=\mathrm{i}_2=\mathrm{i}\)
\(\therefore \mathrm{F}=\frac{\mu_0 \mathrm{i}^2}{2 \pi \mathrm{r}}\)
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