The length and diameter of a uniformly charged cylindrical shell are 4.20 m and 0.165 m, respectively. What net charge on the surface of the cylindrical shell will produce an electric field of 4.90 ✕ 104 N/C at a radial distance of 25.0 cm from the axis of the cylinder?

Electric field at distance r from the axis of a charged cylinder

= λ / 2πε₀ r

where λ is linear charge density

4.9 x 10⁴ = λ / (2π x 8.85 x 10⁻¹² x. 25)

λ = 4.9 x 10⁴ x2π x 8.85 x 10⁻¹² x. 25

= 68.08 x 10⁻⁸ C

Length of cylinder = 4.2 m

Total charge on the cylinder

= 4.2 x 68.08 x 10⁻⁸ C

= 285.95x 10⁻⁸ C