Two small spheres, each of mass 'm' and positive charge 'q', hang from light threads 'l'. Each thread makes an angle with the vertical as shown in the picture...?

(a) draw and label all forces on the sphere 'I'
(b) express how each of the following changes would affect the angle theta
(i) m is decreased ( q and l remain unchanged)
(ii) q is decreased ( m and l remain unchanged)
(iii) l is decreased (q and m remain unchanged)enter image source here

1 Answer
Jun 2, 2018

(a) T, tension in the thread; mg, weight of sphere and
Fe, Coulomb's force of repulsion.
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(b) When the system is in equilibrium, magnitudes of vertical forces and horizontal forces balance each other respectively.
Vertical:

mg=Tcosθ ......(1)

Horizontal:

14πε0q2(2lsinθ)2=Tsinθ
14πε0q24l2sin2θ=Tsinθ .....(2)

Dividing (2) with (1) we get

sinθcosθ=14πε0q24l2sin2θ×1mg
sin3θcosθ=14πε0q24l2mg ......(3)

Exercise: Write down answers to (i) to (iii)