Question

An infinite line of charge with charge density λ1 = -2 μc/cm is aligned with the y-axis as shown. 1) what is ex(p), the value of the x-component of the electric field produced by

Answer 1

The electric field due to an infinite line of charge with a uniform charge density λ can be calculated using Gauss's Law, with the magnitude given by E = λ / (2πε₀r). The field's direction is radial relative to the line of charge and requires understanding of electric flux and vector calculus for more complex calculations.

Step-by-step explanation:

The question relates to the calculation of the electric field (E-field) produced by a continuous distribution of charge. Specifically, it concerns an infinite line of charge, which is a common theoretical model used in physics to simplify the study of electric fields. To calculate the E-field at a point P due to an infinite line of charge with uniform charge density λ, one can use Gauss's Law. This law states that the electric flux through a closed surface is proportional to the enclosed electric charge. For an infinite line charge, one typically considers a cylindrical Gaussian surface co-axial with the line of charge.

The magnitude of the electric field E at a distance r from an infinite line of charge with charge density λ is given by the expression E = λ / (2πε₀r), where ε₀ is the permittivity of free space. This field points radially outward (or inward if the charge density is negative) from the line of charge. When calculating the work done by the E-field on a moving charge or mapping electric field lines, vector calculus may be required to account for the direction and magnitude of the field at various points in space.

Answer 2

As we know by Gauss's law that

`\int E.dA = (q)/(\epsilon_0)`

so for line charge the gaussian surface is cylindrical in shape

so we will have

`E(2\pi RL) = (\lambda L)/(\epsilon_0)`

now by rearranging the terms

`E = (\lambda)/(2\pi \epsilon_0 R)`

so here we will have to find the x component of electric field so it is given by above equation

`E_x = (\lambda)/(2\pi \epsilon_0 x)`

here x = distance from the wire where we need to find electric field