Home
Class 11
PHYSICS
An infinite dielectric sheet having char...

An infinite dielectric sheet having charge density `sigma` has a hole of radius R in it. An electron is released from point P on the axis of the hole at a distance `sqrt(3)R` from the center. Find the speed with which it crosses the plane of the sheet.
.

Text Solution

Verified by Experts

The correct Answer is:
`v=sqrt((sigma eR)/(m in_(0)))`
From energy conservation
`[(sigma R)/(2 in_(0))-sigma/(2in_(0))xx2R]e=-1/2 mv^(2)`
`-(sigmaRe)/(2in_(0))+(sigmaRe)/in_(0)=1/2 mv^(2)`
`v=sqrt((sigma eR)/(m in_(0)))`
Promotional Banner

Topper's Solved these Questions

  • MISCELLANEOUS

    ALLEN|Exercise Exercise-05(A)|35 Videos

  • MISCELLANEOUS

    ALLEN|Exercise Exercise-05(B)|19 Videos

  • MISCELLANEOUS

    ALLEN|Exercise Exersice-04[A]|34 Videos

  • KINEMATICS (MOTION ALONG A STRAIGHT LINE AND MOTION IN A PLANE)

    ALLEN|Exercise BEGINNER S BOX-7|8 Videos

  • PHYSICAL WORLD, UNITS AND DIMENSIONS & ERRORS IN MEASUREMENT

    ALLEN|Exercise EXERCISE-IV|8 Videos

Similar Questions

Explore conceptually related problems

An infinite dielectric sheet having charge density sigma has a holeof radius R in it. An electrom is released from point P on the axis of the hole at a distance sqrt(3)R from the center. Find the speed with which it crosses the plane of the sheet. .

An infinite dielectric sheet having charge density sigma has a hole of radius R in it. An electron is released on the axis of the hole at a distance sqrt(3)R from the center. Find the speed with which it crosses the center of the hole.

There is a uniformly charged ring having radius R. An infinite line charge (charge per unit length lambda) is placed along a diameter of the ring (in gravity free space). Total charge on the ring Q=4sqrt(2lambda)R . An electron of mass m is released from rest on the axis of the ring at a distance x=sqrt(3) R from the centre. Magnitude of initial acceleration of the electron.

There is a uniformly charged ring having radius R. An infinite line charge (charge per unit length lambda) is placed along a diameter of the ring (in gravity free space). Total charge on the ring Q=4sqrt(2lambda)R . An electron of mass m is released from rest on the axis of the ring at a distance x=sqrt(3) R from the centre. The distance from centre of ring on the axis where the net force on the electron is zero.

A large metallic plate is facing a charged sheet having charge density sigma placed parallel to plate at a distance l from the plate.Potential at point P at a distance x from the sheet is

There is a uniformly charged ring having radius R. An infinite line charge (charge per unit length lambda) is placed along a diameter of the ring (in gravity free space). Total charge on the ring Q=4sqrt(2lambda)R . An electron of mass m is released from rest on the axis of the ring at a distance x=sqrt(3) R from the centre. Potential difference between points A(x=sqrt(3)R) and B(x=R)i.e.(V_(A)-V_(B)) is

An infinitely large non-conducting plane of uniform surface charge density sigma has circular aperture of certain radius carved out from it. The electric field at a point which is at a distance 'a' from the centre of the aperture (perpendicular to the plane) is (sigma)/(2 sqrt(2) in_(0)) . Find the radius of aperture :

Find the position of centre of mass of a uniform disc of radius R from which a hole of radius is cut out. The centre of the hole is at a distance R/2 from the centre of the disc.

A large metallic plate is facing a charged sheet having charge density "sigma" placed parallel to plate at a distance "l" from the plate.Potential at "point "P" at a distance [x" from the sheet is "]