Charge q2 of mass m revolves around a stationary charge q1 in a circular orbit of radius r. The orbital periodic time of q2 would be

Question

Charge q2 of mass m revolves around a stationary charge q1 in a circular orbit of radius r. The orbital periodic time of q2 would be (A)  [ ( 4 π2 mr3 / kq1 q2 ) ] 1/2 (B)  [ ( kq1 q2 / 4 π2 mr3 ) ] 1/2 (C)  [ ( 4 π2 mr4 / kq1 q2 ) ] 1/2 (D)  [ ( 4 π2 mr2 / kq1 q2 ) ] 1/2

Tardigrade Admin · Accepted Answer

( 1/ 4 π ε0) ( q1 q2 / r2 ) = mr ω2 = ( 4 π2 mr / T2) T2 = ( ( 4 π ε0 ) r2 ( 4 π2 mr )/ q1 q2 ) [ ( 4 π2 mr3 / kq1 q2 ) ] 1/2

Q. Charge $q_{2}$ of mass m revolves around a stationary charge $q_{1}$ in a circular orbit of radius r. The orbital periodic time of $q_{2}$ would be

$[\frac{4 π ^{2} m r ^{3}}{k q _{1} q _{2}}]^{1/2}$

$[\frac{k q _{1} q _{2}}{4 π ^{2} m r ^{3}}]^{1/2}$

$[\frac{4 π ^{2} m r ^{4}}{k q _{1} q _{2}}]^{1/2}$

$[\frac{4 π ^{2} m r ^{2}}{k q _{1} q _{2}}]^{1/2}$

$\frac{1}{4 π ε _{0}} \frac{q _{1} q _{2}}{r ^{2}} = m r ω^{2} = \frac{4 π ^{2} m r}{T ^{2}}$
$T^{2} = \frac{( 4 π ε _{0} ) r ^{2} ( 4 π ^{2} m r )}{q _{1} q _{2}}$
$[\frac{4 π ^{2} m r ^{3}}{k q _{1} q _{2}}]^{1/2}$

Q. Charge q2​ of mass m revolves around a stationary charge q1​ in a circular orbit of radius r. The orbital periodic time of q2​ would be

[kq1​q2​4π2mr3​]1/2

[4π2mr3kq1​q2​​]1/2

[kq1​q2​4π2mr4​]1/2

[kq1​q2​4π2mr2​]1/2