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A smooth chute is made in a dielectric s...

A smooth chute is made in a dielectric sphere of radius R and uniform volume charge density. `rho`. A charge particle of mass m and charge -q is placed at the centre of the sphere. Find the time period of motion of the particle?

Text Solution

Verified by Experts

Let the particle displace slightly toward right at a distance
r from the centre. The force acting on the particle is
`vecF = -q vecE, where E = rho/(3epsilon_0)vecr`
`=-(rhoq)/(3epsilon_0) vecr`
or `mveca = -(rhoq)/(3epsilon_0) vecr or veca = -(rhoq)/(3mepsilon_0)vecr`
Hence, the force acting on the particle is making the particles
execute SHM. Comparing with `veca = -omega^2vecr, ` we get
`omega^2 = (rhoq)/(3mepsilon_0)`
Hence, the time period of oscillation of the particle is
`T = 2pi sqrt ((3epsilon_0m)/(rhoq))`.
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