Home
Class 12
PHYSICS
An infinitely long solid cylinder of rad...

An infinitely long solid cylinder of radius ` R` has a uniform volume charge density `rho`. It has a spherical cavity of radius `R//2` with its centre on the axis of cylinder, as shown in the figure. The magnitude of the electric field at the point `P`, which is at a distance `2 R` form the axis of the cylinder, is given by the expression `( 23 r R)/( 16 k e_0)` . The value of `k` is .
.

Text Solution

Verified by Experts

We suppose that the cavity is filled up by a positive as well as negative volume charge of `rho`. So the electric field now produced at P is the superposition of two electric fields
(a) The electric field created due to the infinitely long solid cylinder is
`E_1=(rhoR)/(4epsilon_0)` directed towards the `+Y` direction
(b) The electric field created due to the spherical negative charge density
`E_2=(rhoR)/(96epsilon_0)` directed towards the `-Y` direction.
`:.` The net electric field is
`E=E_1-E_2=1/6[(23rhoR)/(16epsilon_0)]`
Promotional Banner

Topper's Solved these Questions

  • ELECTROSTATICS

    SUNIL BATRA (41 YEARS IITJEE PHYSICS)|Exercise Subjective Problems|2 Videos

  • ELECTROSTATICS

    SUNIL BATRA (41 YEARS IITJEE PHYSICS)|Exercise Comprehension Based Questions|2 Videos

  • ELECTROMAGNETIC INDUCTION AND ALTERNATING CURRENT

    SUNIL BATRA (41 YEARS IITJEE PHYSICS)|Exercise JEE Main And Advanced|107 Videos

  • MODERN PHYSICS

    SUNIL BATRA (41 YEARS IITJEE PHYSICS)|Exercise MCQ (One Correct Answer|1 Videos

Similar Questions

Explore conceptually related problems

An infinitely long solid cylinder of radius R with uniform volume charge density rho has a spherical cavity of radius (R)/(2) with its centre on the axis of the cylinder as shown in the figure. The magnitude of the electric field at a point P which is at a distance 2R from the axis of the cylinder is given by (23rhoR)/(6Kepsilon_(0)) . What is the value of K ?

Inside a uniformly charged infinitely long cylinder of radius 'R' and volume charge density 'rho' there is a spherical cavity of radius 'R//2'. A point 'P' is located at a dsintance 2 R from the axis of the cylinder as shown. Then the electric field strength at the point 'P' is

A cylinder of length L has a charge of magnitude q. The electric intensity at a point at a distance r from the axis of the cylinder is

A solid of radius 'R' is uniformly charged with charge density rho in its volume. A spherical cavity of radius R/2 is made in the sphere as shown in the figure. Find the electric potential at the centre of the sphere.

A positively charged sphere of radius r_(0) carries a volume charge density rho_(E) (Figure). A spherical cavity of radius r_(0)//2 is then scooped out and left empty, as shown. What is the direction and magnitude of the electric field at point B?

A solid sphere having radius R and uniform charge density rho has a cavity of radius R/2 as shown in figure.Find the value of |E_A /E_B|

An infinity long cylinder of radius R has an infinitely long cylindrical cavity of radius (R)/(2) are shown in the figure. The remaining portion has uniform volume charge density rho . The magnitude of electrical field at the centre of the cavity is-

An insulated sphere of radius r haas a uniform volume charge density lambda . The electric field at a point A , which is at distance r from its centre is given by (R gt r)