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Electrostatics — Physics STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 SciencePhysicsElectrostatics1 Mark
MCQ
A uniformly charged semicircular arc of radius $'r\ '$ has linear charge density $' \lambda\ ' $.The electric field at its centre is $($ $\varepsilon_0=$ permittivity of free space$)$
  • A
    $\frac{\lambda}{4 \varepsilon_0}$
  • B
    $\frac{2 \varepsilon_0}{\lambda}$
  • ✓
    $\frac{\lambda}{4 \varepsilon_0 r}$
  • D
    $\frac{2 \pi \varepsilon_0}{\lambda}$
✓

Answer

Correct option: C.
$\frac{\lambda}{4 \varepsilon_0 r}$
The electric field due to a small element,
$E=\frac{k d q}{r^2}$
$=\frac{1}{4 \pi \varepsilon_0} \frac{\lambda \cdot \pi r}{r^2}$
$E=\frac{\lambda}{4 \varepsilon_0 r}$

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