Question

A charged wire of negligible thickness has length 2L units and has a linear charge density λ. Consider the electric field E-vector at the point P, a distance d above the midpoint of the wire. The field E-vector points along one of the primary axes, yWhat is the magnitude E of the electric field at point P? Throughout this part, express your answers in terms of the constant k, defined by k=1/(4πε)

Answer 1

`E=2K\lambda d(L )/(d^2√(L^2+d^2))`

Step-by-step explanation:

Given that

Length= 2L

Linear charge density=λ

Distance= d

K=1/(4πε)

The electric field at point P

`E=2K\int_(0)^(L)(\lambda )/(r^2)dx\ sin\theta`

`sin\theta =(d)/(√(d^2+x^2))`

`r^2=d^2+x^2`

So

`E=2K\lambda d\int_(0)^(L)\frac{dx }{(x^2+d^2)^{(3)/(2)}}`

Now by integrating above equation

`E=2K\lambda d(L )/(d^2√(L^2+d^2))`