An oil drop having charge #q# and apparent weight #W# falls with a terminal speed #v# in the absence of electric field. When electric field is switched on it starts moving up with terminal speed #v#. The strength of the electric field is ??
1 Answer
The drag force acting upon the oil drop is calculated from Stoke's law and is given as
#F_d=6pietarv# ......(1)
The apparent weight for a perfectly spherical body is given by
True weight
#F_barg=W# .....(2)
At terminal velocity the oil drop is not accelerating as the net force acting on it must be zero
#F_d-F_barg=0#
Hence equating (1) and (2) we get
#W=6pietarv_(Tdarr)# ......(3)
where#r# -radius of oil drop,#η# -viscosity of air,#v_(Tdarr)# -terminal velocity.
When electric field
Electric force will act upwards, net gravity and drag forces acts downwards. Net force acting on the oil drop is again zero.
#F_e-F'_d-F_barg=0#
#=>F_e=F'_d+F_barg=0#
where
Inserting various values above expression becomes
#qE=6pietarv_(Tuarr)+W#
Given
#:.qE=W+W#
#=>E=(2W)/q# ......(4)
.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-
Apparent weight in terms of other variables.
#F_barg=4/3pir^3g(rho-rho_(air))=W# .....(2)
Hence equating (1) and (2) we get
#r^2=(9etav_(Tdarr))/(2g(rho-rho_(air))# ......(3)
where#r# -radius of oil drop,#η# -viscosity of air,#v_(Tdarr)# -terminal velocity,#g# - acceleration due to gravity,#ρ# -density of oil and#ρ_(air)# -density of air