Question

in rind the Mass of the Earth Problem 3. A "semi-infinite" non-conducting rod (that is, infinite in one direction only) has uniform linear charge density a. Show that the electric field at point P makes an angle of 45° with the rod and that this result is independent of the distance R Hint: Separately find the parallel and perpendicular (to the rod) components of the electric field at then compare those components P, and

Answer 1

The x and the y components of the electric field at point P will be as shown below:

Now,

the x component will be

By integrating we get

similarly the y component of the electric field will be

by intergrating we get

Now the angle will be

by plugging all the values we get

which gives us

or

which is independent of R