TeXercises.com

Charged Ring

About points...

We associate a certain number of points with each exercise.
When you click an exercise into a collection, this number will be taken as points for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit the number of points for the exercise in the collection independently, without any effect on "points by default" as represented by the number here.

That being said... How many "default points" should you associate with an exercise upon creation?
As with difficulty, there is no straight forward and generally accepted way.
But as a guideline, we tend to give as many points by default as there are mathematical steps to do in the exercise.
Again, very vague... But the number should kind of represent the "work" required.

About difficulty...

We associate a certain difficulty with each exercise.
When you click an exercise into a collection, this number will be taken as difficulty for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit its difficulty in the collection independently, without any effect on the "difficulty by default" here.
Why we use chess pieces? Well... we like chess, we like playing around with \(\LaTeX\)-fonts, we wanted symbols that need less space than six stars in a table-column... But in your layouts, you are of course free to indicate the difficulty of the exercise the way you want.

That being said... How "difficult" is an exercise? It depends on many factors, like what was being taught etc.
In physics exercises, we try to follow this pattern:

Level 1 - One formula (one you would find in a reference book) is enough to solve the exercise. Example exercise

Level 2 - Two formulas are needed, it's possible to compute an "in-between" solution, i.e. no algebraic equation needed. Example exercise

Level 3 - "Chain-computations" like on level 2, but 3+ calculations. Still, no equations, i.e. you are not forced to solve it in an algebraic manner. Example exercise

Level 4 - Exercise needs to be solved by algebraic equations, not possible to calculate numerical "in-between" results. Example exercise

Level 5 -
Level 6 -

Exercise

https://texercises.com/exercise/charged-ring-1/

Question

Solution

Short

Video

\(\LaTeX\)

No explanation / solution video to this exercise has yet been created.

Visit our YouTube-Channel to see solutions to other exercises.
Don't forget to subscribe to our channel, like the videos and leave comments!

Exercise:
A ring with radius RO carries a uniformly distributed charge of QO. A qO po charge is placed on the ring's central axis. abcliste abc Calculate the force acting on the po charge for a distance dO from the ring. Compare the result with the result you would get using Coulomb's law. abc Show with a formal calculation that for large distances dgg R the expression for the force between the ring and the po charge approaches Coulomb's force law. abcliste

Solution:
abcliste abc The force between the charged ring and the po charge is see notes: F FF kCtimesfracQtimes qtimes dleftR^+d^right^/ F approx resultFP- Using Coulomb's law we find F_C FCF kCtimesfracQtimes qd^ FC approx resultFCP- This is percerrP larger than the correct result. Coulomb's law overestimates the result because it ases that the charge of the ring is concentrated at a distance d dO from the po charge which is smaller than the real distance. abc By factorin out d^ in the numerator we can write the force as F k_CfracQ q dd^leftR/d^+right^/ For Rgg d the ratio R/d is much less than so we can approximate the force as F &approx k_CfracQ q dd^leftright^/ FCF This is the expression for Coulomb's law. abcliste

Meta Information

\(\LaTeX\)-Code

Contained in these collections:

Electric Charge and Electric Force by by

10 | 16

Attributes & Decorations

Branches	Electrostatics
Tags	coulomb law, electrostatic force
Content image
Difficulty	(2, default)
Points	0 (default)
Language	(English)
Type	Calculative / Quantity
Creator	by
Decoration
File
Link