A simple pendulum is having bob of mass m carrying a charge q and is hanging from ceiling. A uniform electric field E is applied in downward direction then time period of simple pendulum is.

Asked by ruchiaggarwal083 | 12th May, 2021, 08:47: AM

Expert Answer:

Period of simple pendulam in absence of electric field is given as
 
begin mathsize 14px style T space equals space 2 pi square root of l over g end root end style
where l is length of simple pendulam and g is acceleration due to gravity.
 
When the electric field is present , in addition to gravitational force ,
we have force (qE ) due to electric field in the same direction of gravitational force.
Hence downward acceleration due to this electric field is force / mass  = [ ( qE ) / m ]
 
where q is the charge on the bob of pendulam , E is electric field intensity and m is mass of pendulam
 
Hence change in period T of simple pendulam is given as
 
begin mathsize 14px style T space equals space 2 pi square root of fraction numerator l over denominator g apostrophe end fraction end root space equals space 2 pi square root of fraction numerator l over denominator open parentheses g space plus space begin display style fraction numerator q E over denominator m end fraction end style close parentheses end fraction end root end style
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Second question
 
Force F between two charges of equal magnitude q is given as
 
begin mathsize 14px style F space equals space fraction numerator q squared over denominator 4 pi epsilon subscript o d squared end fraction end style.................................(1)
Since force F is directly proportional to square of charge magniude,
charge magnitude has to be made as 2q to get force 4F .
 
Hence increase in charge = q
 
From eqn.(1), we get q as

begin mathsize 14px style q space equals space square root of 4 pi epsilon subscript o d squared end root end style..........................(2)
if e is charge on electron, number of electrons n is to be added is determined as
 
begin mathsize 14px style q space equals space n space e space equals space space square root of 4 pi epsilon subscript o d squared end root end style
Hence we get ,  begin mathsize 14px style n space equals space square root of fraction numerator 4 pi epsilon subscript o F d squared over denominator e squared end fraction end root end style

Answered by Thiyagarajan K | 12th May, 2021, 02:19: PM