A positively charged particle of charge q and mass m is suspended from a point by a string of length l. In the space a uniform horizontal electric field E exists. The particle is drawn aside so that the string becomes vertical and then it is projected horizontally with velocity v such that the particle starts to move along a circle with same constant speed v. Find the speed v.
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a
2qEmlg
b
qEmlg
c
qEm2lg
d
qE2mlg
answer is B.
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Detailed Solution
θ is equilibrium position. Net force in equilibrium positionF=(mg)2+(qE)2tanθ=qEmgTcosθ=FTsinθ=mv2rwhere r=lsinθSolve to get v=qEmlg