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
A08
Jun 2, 2018

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

#mg=Tcostheta# ......(1)

Horizontal:

#1/(4piepsilon_0)q^2/(2lsintheta)^2=Tsintheta#
#1/(4piepsilon_0)q^2/(4l^2sin^2theta)=Tsintheta# .....(2)

Dividing (2) with (1) we get

#sintheta/costheta=1/(4piepsilon_0)q^2/(4l^2sin^2theta)xx1/(mg)#
#=>sin^3theta/costheta=1/(4piepsilon_0)q^2/(4l^2mg)# ......(3)

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

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