First slide

Electric field

Question

Three identical point charges, each of mass m and charge q, hang from three strings as shown in figure. The value of q in terms of m, L, and q is

Moderate

A

$q = \sqrt{(16 / 5) π ε_{0} m g L^{2} \sin^{2} θ \tan θ}$
B

$q = \sqrt{(16 / 15) π ε_{0} m g L^{2} \sin^{2} θ \tan θ}$
C

$q = \sqrt{(15 / 16) π ε_{0} m g L^{2} \sin^{2} θ \tan θ}$
D

none of these

Solution

$\begin{array}{l} F_{e} = F_{2} + F_{3} \\ = \frac{k q^{2}}{(L \sin θ)^{2}} + \frac{k q^{2}}{(2 L \sin θ)^{2}} \\ F_{e} = \frac{5}{4} \frac{k q^{2}}{L^{2} \sin^{2} θ} . . . . . . (i) \\ T \sin θ = E e . . . . . . (i i) \\ T \cos θ = m g . . . . . . . . (i i i) \end{array}$
From (i), (ii), and (iii)
$q = \sqrt{\frac{16}{5} π ε_{0} m g L^{2} \sin^{2} θ \tan θ}$

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