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An infinite line of charge produces a field of magnitude4.5×104N/Cat distance 2.0 m. Find the linear charge density.

Short Answer

Expert verified

The linear charge density is 5.0×10-6C/m.

Step by step solution

01

The given data

  1. Magnitude of an electric field,E=4.5×104N/C
  2. Distance of the line from the electric field,r=2.0m
02

Understanding the concept of the electric field

Using the concept of the electric field of a cylindrical Gaussian surface, we can get the required value of the linear charge density by substituting the given data.

Formula:

The electric field of a cylindrical Gaussian surface,E=λ2πε0r (1)

03

Calculation of the linear charge density

Substituting the given values in equation (1), we can get the required value of the uniform linear density on the line as follows:

λ=2πε0rE=2π8.85×10-12C2/N.m24.5×104N/C2.0m=5.0×10-6C/m

Hence, the value of the linear density is 5.0×10-6C/m.

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