Question

(1) In this problem, we will calculate the electric ?eld of a line charge. The line charge is aligned along the x-axis starting at the origin and having a length L. The line has a linear charge density ?. We want to ?nd the electric ?eld at a point P on the x-axis. The point P is located at the point pd,0q where d?L. (a) List all of the given parameters. (b) What is the dimensionality of a line of charge? What is the electric ?eld of a small charge dq which is one dimension less than our line? (c) What is the charge dq in terms of the given parameters? (d) What is the distance between an arbitrary point on our line charge to the point P in terms of given parameters? (e) What is the unit vector

Answer 1

a) in this problem

consider the line is having charge q

assume that positive charge

use basic law that is gauss

flux comming from the surface which is due to enclosing the charge

lamda(it denotes the line charge density)

E is electric field

b) dimensions of line charge density is charge/unit length

c) integration of electricfield around the surface equals to=line charge density*length/epsilon

dq=lamda*dl

d) we need to calculate distance from origin

so d=l

e) unit vector it is indicated by r bar so r=dx*i bar

=dl*i bar

f)

• A cylinder centered on the axis of the line charge is the best choice since the E-field is constant on the outer wall of any cylinder and zero on the ends of the cylinder. This choice makes doing the integration to find the electric flux easy.

• Letting L be the length of the cylinder,

g, f) combined electric field will be

• The charge Q_inside can be found using the charge density l and the length L , Q^_inside = l L. Solving for E in Gauss