Question

The surface charge density of an infinitely
long cylinder is 2microC/m² and the linear
density of charge along the cylinder is
2nC/cm. The circumference of the plane
surface of cylinder is
1) 10 cm
2) 0.001 m
3) 1000 cm
4)10/2pi m​

Answer 1

Answer:

Gauss's law states that " total electrical flux through a closed surface equals the charge contained in the enclosed volume divided by εo "

( εo is the permitivity of the medium enclosed by the surface)

 

Mathematically, begin mathsize 12px style contour integral E times d a space equals space q over epsilon subscript o end style ................(1)

It is assumed the charged cylinders are infinitely long.  

 

To get electric field inside the charged coaxial cylinders, we consider an imaginary cylinder of radius r1 and of length l1 as shown in figure.

Due to infilint length, electric field is perpendicular to the curved surface of this imaginary cylinder and the field is uniform.  

hence eqn.(1) can be written for this imaginary cylinder as,

 

Er × 2πr1l1  = (λ1 × l1 ) / εo or Er = λ1 / ( 2πεor1 )  

(subscript r is used to indicate, field is in radial direction)

 

In same way electric field at a point outside the larger radius cylinder, Er = ( λ1 - λ2 )/ ( 2πεor2 )