What is the electric field inside and outside a long cylinder of aluminum with a uniform charge per unit length on its surface?

Question

Joanny · Answer

Electric Field Inside the Cylinder     Main answer: The electric field inside the charged cylinder of radius R with uniform charge per unit length on its surface is zero.          Electric Field Outside the Cylinder     Main answer: The electric field outside the cylinder is given by E = λ/(2πε₀r), where λ is the linear charge density, r is the distance from the center of the cylinder, and ε₀ is the electric constant.          Supporting explanation: According to Gauss's law, the electric field inside a closed surface is proportional to the enclosed charge. Since the cylinder has no charge inside it, the electric field inside the cylinder is zero. Outside the cylinder, the electric field is radial and directed away from the cylinder. The electric field is proportional to the linear charge density on the cylinder and inversely proportional to the distance from the center of the cylinder. Therefore, the electric field outside the cylinder can be expressed as E = λ/(2πε₀r), where λ = 1 is the linear charge density.

Electric Field Inside and Outside a Charged Cylinder

Electric Field Inside the Cylinder

Electric Field Outside the Cylinder

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