Q134 / 150 · MHT CET 2022 (07 Aug Shift 2) · Physics

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
  • Correct answer
    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

Solution

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 $\mathrm{i}_1=\mathrm{i}_2=\mathrm{i}$ $\therefore \mathrm{F}=\frac{\mu_0 \mathrm{i}^2}{2 \pi \mathrm{r}}$

Hence, the correct answer is option: 'C'.

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