Home
Class 12
PHYSICS
A very long, solid insulating cylinder w...

A very long, solid insulating cylinder with radius R has a cylindrical hole with radius a bored along its entire length. The axis of the hole is at a distance b from the axis of the cylinder, where `altbltR` (as shown in figure). The solid material of the cylinder has a uniform volume charge density `rho`. Find the magnitude and direction of the electric field inside the hole, and show that this is uniform over the entire hole.
.

Text Solution

Verified by Experts

The correct Answer is:
`(rho)/( 2 epsilon_(0)) vec(b)`
`vecE _("whole") = vecE_("cylinder") - vecE_("hole")`
`= (rhovecr)/(2epsilon_0) - (rhovecs)/(2epsilon_0) = rho/(2epsilon_0) (vecr - vecs) = (rho)/(2epsilon_0) vecb`
Note that `vecE_(whole)` is uniform within the hole.
Promotional Banner

Topper's Solved these Questions

  • ELECTRIC FLUX AND GAUSS LAW

    CENGAGE PHYSICS ENGLISH|Exercise Single Correct|40 Videos

  • ELECTRIC FLUX AND GAUSS LAW

    CENGAGE PHYSICS ENGLISH|Exercise Multiple Correct|8 Videos

  • ELECTRIC FLUX AND GAUSS LAW

    CENGAGE PHYSICS ENGLISH|Exercise Exercise 2.2|14 Videos

  • ELECTRIC CURRENT AND CIRCUIT

    CENGAGE PHYSICS ENGLISH|Exercise Interger|8 Videos

  • ELECTRIC POTENTIAL

    CENGAGE PHYSICS ENGLISH|Exercise DPP 3.5|15 Videos

Similar Questions

Explore conceptually related problems

A non-conducting sphere of radius R has a spherical cavity of radius R//2 as shown. The solid part of the sphere has a uniform volume charge density rho . Find the magnitude and direction of electric field at point (a) O and (b) A.

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-

The moment of inertia of cylinder of radius a, mass M and height h about an axis parallel to the axis of the cylinder and distance b from its centre is :

A thin but long, hollow, cylindrical tube of radius r carries a current i along its length. Find the magnitude of the magnetic field at a distance r/2 from the surface (a) inside the tube (b) outside the tube.

A long cylindrical conductor of radius R having a cylindrical cavity of radius R/2 through out its length is lying with its axis parallel to x-axis. The distance between the axes of the cylinder and the cavity length in the positive x direction. The across sectional view of the cylinder is shown in the figure The magnetic induction at point on the cavity is

A cylinder of radius R and length l is placed in a uniform electric field E parallel to the axis of the cylinder. The total flux over the curved surface of the cylinder is

How does the electric field (E) between the plates of a charged cylindrical capacitor vary with the distance r from the axis of the cylinder ?

A long thin hollow metallic cylinder of radius 'R' has a current i ampere. The magnetic induction 'B' -away from the axis at a distance r from the axis varies as shown in

Consider a cylindrical surface of radius R and length l in a uniform electric field E. Compute the electric flux if the axis of the cylinder is parallel to the field direction.

Find the moment of inertia of a solid cylinder of mass M and radius R about a line parallel to the axis of the cylinder and on the surface of the cylinder.