Electrostatics 1 Question 17

18. An infinitely long solid cylinder of radius R has a uniform volume charge density ρ. It 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 the point P, which is at a distance 2R from the axis of the cylinder, is given by the expression 23ρR16kε0.

The value of k is

(2012)

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Answer:

Correct Answer: 18. (b)

Solution:

  1. Volume of cylinder per unit length (l=1) is

V=πR2l=(πR2)

Charge per unit length,

λ=( Volume per unit length )×( Volume charge density )

=(πR2ρ)

Now at P

R= Remaining portion

ER=ETEC

T= Total portion and

C= cavity

ER=λ2πε0(2R)14πε0Q(2R)2Q= charge on sphere =43πR32ρ=πR3ρ6

Substituting the values, we have

ER=(πR2ρ)4πε0R14πε0(πR3ρ/6)4R2=23ρR96ε0=23ρR(16)(6)ε0k=6



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