Question

1.A continuos line of charge lies along the x axis, extending from x= x0.to positive infinity.the line carries positive charge with a uniform linear charge density.what are (a) magnitude and b) direction of electric field at the origin.

2.consider a long cylindrical charge distribution of radius R with a uniform charge density p.find the electric field at distance r from the axis where r<R

3.a solid sphere of radius 40.0cm has a total positive charge of 26.0 uniformly distributed throughout it's volume calculate the magnitude of the electric field a)0cm b)10.0 cm c)40.0 cm d)60.0 cm from the centre of sphere

Answer 1

1.)

Here we have to find the electric field vector at origin then the r=x₀ and the direction of electric field will be in the direction of negative x as every small part of the rod is creating electric field in negative x at origin

let the linear charge charge density of the rod be $\lambda$

$dE=k\smallint\frac{\lambda dx}{x^2}$

$E=k\smallint^{x_0}_{\infin}\frac{\lambda dx}{x^2}$

$E=\dfrac{k\lambda}{x_o}(-i)$