An infinitely long line of charge with uniform density, rho lies in y-z plane parallel to the zaxis at y=1m. (a) Find the potential VAB at point A (4m, 2m, 4m) in Cartesian coordinates with respect to point B (0,0,0). (b) Find E filed at point B.

Answer with Explanation:

We are given that

Density=

A(4m,2m,4m) and B(0,0,0)

y=1 m

a. Linear charge density=

Let a point P (0,1,4) on the line of charge  and point Q (0,1,0)

Therefore,

Distance AP=

Distance,BQ=

Electric field for infinitely long line

Therefore, potential

b.Electric field at point B

Unit vector r=

Therefore,