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1. Electric charges and fields — Physics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 SciencePhysics1. Electric charges and fields1 Mark
MCQ
A wheel having mass $m$ has charges $+q$ and $-q$ on diametrically opposite points. It remains in equilibrium on a rough inclined plane in the presence of a vertical electric field $E$. Then value of $E$ is
  • A
    $\frac{{mg}}{q}$
  • ✓
    $\;\frac{{mg}}{{2q}}$
  • C
    $\;\frac{{mgtan\theta }}{{2q}}$
  • D
    $\;\frac{{mgtan\theta }}{q}$
✓

Answer

Correct option: B.
$\;\frac{{mg}}{{2q}}$
b
The torque of electric force about centre is balanced by torque due to friction about the centre

$r f ={ PE } \sin \theta$

$\tau= PE \sin \theta$

$\text { But } f = mg \sin \theta$

$mgr \sin \theta= PE \sin \theta$

$E =\frac{ mgr }{ P }=\frac{ mgr }{ q \times 2 r }$

$P = q \times 2 r (\text { dipole moment })$

$E =\frac{ mg }{2 q }$

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