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

Question

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 2 R from the axis of the cylinder, is given by the expression 16 K ε 0 ​ 23 ρR ​ . The value of k is

TestHub · Accepted Answer

The magnitude of the electric field at the point P which is at a distance 2 R from the axis of the cylinder E = E total ​ − E cavity ​ = 2 π ε 0 ​ ( 2 R ) γ ​ − 4 π ε 0 ​ 1 ​ ( 2 R ) 2 Q ​ Q sphere ​ = 3 4 ​ π ( 2 R ​ ) 3 ρ = 6 π R 3 ρ ​ λ cylinder ​ = π R 2 ρ ∴ E = 4 π ε 0 ​ R π R 2 ρ ​ − 4 π ε 0 ​ 1 ​ ⋅ 4 R 2 π R 3 ρ /6 ​ = 96 ε 0 ​ 23 ρR ​ = 16 × 6 × ε 0 ​ 23 ρR ​ ∴ k = 6 ​ ​

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