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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 | 12 May, 2021, 08:47: AM
Period of simple pendulam in absence of electric field is given as

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

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Second question

Force F between two charges of equal magnitude q is given as

.................................(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

..........................(2)
if e is charge on electron, number of electrons n is to be added is determined as

Hence we get ,
Answered by Thiyagarajan K | 12 May, 2021, 02:19: PM

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