Q162 / 180 · KCET 2023 · Physics

Electric field at a distance $r$ from an infinitely long uniformly charged straight conductor, having linear charge density $\lambda$ is $E_1$. Another uniformly charged conductor having same linear charge density $\lambda$ is bent. into a semicircle of radius $r$. The electric field at its centre is $E_2$. Then

  • A
    $E_2=\pi r E_1$
  • B
    $E_2=\frac{E_1}{r}$
  • Correct answer
    C
    $E_1=E_2$
  • D
    $E_1=\pi r E_2$

Solution

Electric field due to infinitely charged long wire, $E_1=\frac{2 k \lambda}{r}$. Electric field at the centre of semicircular ring, $E_2=\frac{2 k \lambda}{r}$ Therefore, $E_1=E_2$

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

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