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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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Text Solution

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`E_(1)=(lambda)/(2piepsilon_(0)2R)=(rhopiR^(2))/(4piepsilon_(0))=(rhoR)/(4epsilon_(0))`
`E_(2)=1/(4piepsilon_(0)) (rho.4/3 pi.(R^(3))/8)/((2R)^(2))`
`E_(1)-E_(2)=(rhoR)/(4epsilon_(0))-(rhoR)/(epsilon_(0).24xx4)=(rhoR)/(4epsilon_(0))[1-1/24]`
`=(23 rhoR)/(96 epsilon_(0))=(23rhoR)/(16 k epsilon_(0)) :. k=6`
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