A stationary electric dipole ϕ = pk is situated at origin. A positive charge q, mass m executes circular motion of radius s at constant speed in the field of the dipole. Mark the correct statement r

Question

A stationary electric dipole ϕ ​ = pk is situated at origin. A positive charge q, mass m executes circular motion of radius s at constant speed in the field of the dipole. Mark the correct statement regarding the plane of orbit :-

TestHub · Accepted Answer

For constant speed the dipole's force on q must be purely centripetal, so the orbit is a circle of radius s in a plane parallel to the equatorial plane, centred on the dipole axis at height z where $E_{z} = 0$ : $3 z^{2} = s^{2} + z^{2}$ ⇒ $z = \frac{s}{2}$ .

There $r^{2} = \frac{3 s ^{2}}{2}$ and the radial field is $\frac{3 k p zs}{r ^{5}}$ : $\frac{m v ^{2}}{s} = \frac{3 k pq zs}{r ^{5}}$ ⇒ $v = \frac{1}{s} \frac{qp}{3 3 π ε _{0} m}$ - (B)

$L = m v s = \frac{qp m}{3 3 π ε _{0}}$ - (D)

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