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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 .
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Knowledge Check

  • 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
    `(23rhpR)/(54varepsilon_(0))`
    B
    `(23rhpR)/(108varepsilon_(0))`
    C
    `(25rhoR)/(54varepsilon_(0))`
    D
    `(25rhoR)/(108varepsilon_(0))`

  • 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

  • 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
    `(17rhor_(0))/(54in_(0)) l eft`
    B
    `(rho_(0))/(6in_(0))l eft`
    C
    `(17rhor_(0))/(54in_(0))right`
    D
    `(rhor_(0))/(6in_(0)) right`

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