Purchase Solution

# Electric field/binomial expansion?

Not what you're looking for?

Show that, for points that are far from a hoop of charge q and radius r, the electric field looks like a point charge.
Show this using a diagram and use binomial expansion.

I'm not sure if I am setting this up correctly, and I really need help on the binomial expansion. Thank you.

##### Solution Summary

The expert uses binomial expansion to examine electric fields.

##### Solution Preview

Let us consider a charged hoop of radius r with charge q uniformly distributed over it. Charge per unit length of the hoop = σ = Total charge/Circumference = q/2Πr ...(1)

Let us consider a segment of length dl of the hoop as shown in the fig..
Charge on the segment = dq = σdl ...(2)

Electric field intensity at point P on the hoop's axis (distant x from the centre of the hoop and distant s from the segment dl) = dE = (1/4Πε0) dq/s2

Substituting for dq from (2) we get: dE = (1/4Πε0) σdl/s2 ...(3)

Vector dE can be resolved into ...

##### Introduction to Nanotechnology/Nanomaterials

This quiz is for any area of science. Test yourself to see what knowledge of nanotechnology you have. This content will also make you familiar with basic concepts of nanotechnology.

##### Variables in Science Experiments

How well do you understand variables? Test your knowledge of independent (manipulated), dependent (responding), and controlled variables with this 10 question quiz.

##### Intro to the Physics Waves

Some short-answer questions involving the basic vocabulary of string, sound, and water waves.

##### Classical Mechanics

This quiz is designed to test and improve your knowledge on Classical Mechanics.

##### The Moon

Test your knowledge of moon phases and movement.