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A solid sphere uniformly charged has a long smooth tunnel passing through it, at a distance of r from the centre of the sphere(assume it to be a chord). A charged particle -Q,mass m is released in the tunnel at a distance x from the centre of the tunnel. Find the time required by the particle to reach the centre of the tunnel if charge of the sphere is Q and radius is R.

A solid sphere uniformly charged has a long smooth tunnel passing through it, at a distance of r from the centre of the sphere(assume it to be a chord). A charged particle -Q,mass m is released in the tunnel at a distance x from the centre of the tunnel. Find the time required by the particle to reach the centre of the tunnel if charge of the sphere is Q and radius is R.

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1 Answers

Arun Kumar IIT Delhi
askIITians Faculty 256 Points
9 years ago
Distance of chord from center = r
Radius of Sphere = R
Distance of particle from center of tunnel = x
Distance of particle from center

Now the electric field effective on that particle will be with a sphere of above radius and charge proptional to volume of sphere with above volume(Apply Gauss law)
But the direction of this force will be radial .
So Take tunnel direction component.
Divide by mass to get acceleration.

Then get the time.

Thanks & Regards
Arun Kumar
IIT Delhi
Askiitians Faculty

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