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(a) There is a long uniformly charged cy...

(a) There is a long uniformly charged cylinder having a volume charge density of `rho C//m^3`. Radius of the cylinder is R. Find the electric field at a point at a distance x from the axis of the cylinder for following cases (i) x lt R (ii) x gt R What is the maximum field produced by the charge distribution at any point? (b) The cylinder described in (a) has a long cylindrical cavity. The axis of cylindrical cavity is at a distance a from the axis of the charged cylinder (see figure). Find electric field inside the cavity.

Text Solution

Verified by Experts

The correct Answer is:
(a). (i) `(rhox)/(2epsilon_(0)x)`
(ii) `(rhoR^(2))/(2epsilon_(0)x)` field at the surface is maximum
`E_(max)=(rhoR)/(2epsilon_(0))`
(b). `vecE=(rhoveca)/(2epsilon_(0))`
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Knowledge Check

  • There is a long, uniformly charged, non-conducting solid cylinder.

    A
    The magnitude of electric field intensity at any point inside the cylinder is directly proportional to the length of perpendicular drawn from a point on the axis of cylinder.
    B
    The magnitude of electric field intensity at any point outside the cylinder is inversely proportional to the length of perpendicular drawn from a point on the axis of cylinder.
    C
    Electric field intensity in not defined for the points on the axis of cylinder
    D
    Electric field intensity is zero for the points on the axis of cylinder

  • 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
    `E=1/(4piin_(0)K)*q/(r^(2))`
    B
    `E=1/(2piin_(0)k)*q/(rL)`
    C
    `E=sigma//in_(0)k`
    D
    none of these

  • If sigma is surface density of charge on the charged cylinder of radius R, then electric intensity E at outer point at a distance r from its axis is

    A
    `(sigmaR)/(in_(0)kr)`
    B
    `(sigmar)/(in_(0)kR)`
    C
    `(sigma)/(in_(0)k)`
    D
    `(sigma^(2)R)/(in_(0)kr)`

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