An imaginary cylinder with radius 0.25 m and length 0.4 m has an infinite line of positive charge running along its axis. The charge per unit length on the line is 3.0 micro coulomb per meter. What is the electric flux through the cylinder due to this infinite line of charge?

Φ = 1.356 × 10^(6) N.m²/C

Explanation:

We are given;

Radius; r = 0.25 m

Length; L = 0.4 m

charge per unit length; λ = 3.00 μC/m = 3 × 10^(-6) C/m

The formula for the electric flux is given by;

Φ = EA cos θ

Since it's normal to the curved surface of the cylinder, then θ = 0.

Thus;

Φ = EA cos 0

Φ = EA

Now, E is expressed as; E = λ/(2π*ε_o*r)

The Area, A = 2πrL

Thus;

Φ = EA = λ/(2π*ε_o*r) × 2πrL

Φ = λL/ε_o

ε_o is a constant known as vacuum permittivity and has a value of 8.85 × 10^(−12) C²/N.m²

Thus;

Φ = (3 × 10^(-6) × 0.4)/(8.85 × 10^(−12))

Φ = 1.356 × 10^(6) N.m²/C

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