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Q. 52

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 685

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Short Answer

The electric field must be zero inside a conductor in electrostatic equilibrium, but not inside an insulator. It turns out that we can still apply Gauss's law to a Gaussian surface that is entirely within an insulator by replacing the right-hand side of Gauss's law, with , where is the permittivity of the material. (Technically, is called the vacuum permittivity.) Suppose a long, straight wire with linear charge density is covered with insulation whose permittivity is . What is the electric field strength at a point inside the insulation that is from the axis of the wire?

The electric field at distance is

See the step by step solution

Step by Step Solution

Step 1: Electric flux

The amount of electric field that flows through some kind of closed surface is called as the electric flux. The electric field through a surface is related to the charge inside the surface, as per Gauss's law. Because of electric field is uniform here, we can calculate the electric flux with equation (24.3).

Additionally, the electric field is proportional to the charge by

The electric field which is related to the charge by

Step 2: Flux through the wire

The wire with charge density and length is

Since the wire's top and bottom edges are proportional to the direction field, the flux into them is zero, whereas its flux through the wire's wall is greatest. As a conclusion, we gain flux via the wire by

Step 3: The electric field at distance

From equations and , we calculate the electric field by

So, the electric field at distance is

We are given that and . So, we plug the values for , and to get by

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