Is My Calculation of Electric Field Correct Using the Paint Document?

AI Thread Summary
The calculation of the electric field is based on the equations v = kq/r and E = kq/r^2. The user is confused about their result of 2500 for E, noting that the potential changes non-linearly between circles. It is emphasized that the electric field is derived from the negative potential gradient, -ΔV/Δd. To accurately determine E, both circles above and below the point of interest should be considered. Clarifying these concepts will help correct the calculation.
Miike012
Messages
1,009
Reaction score
0
The question is in the paint doc...

What I did...

1st eq.
v = kq/r

q = vr/k

2nd equ.

E = kq/r^2

where am I going wrong...? For E I am getting 2500
 

Attachments

  • ph.jpg
    ph.jpg
    17.4 KB · Views: 408
Physics news on Phys.org
The potential is not linear function of the distance, it changes 25 V from the second circle to the third one, and 50 V from the third circle to the fourth. The electric field is negative potential gradient, -ΔV/Δd. Use both circles, below and above the point shown to get it.

ehild
 
I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
Essentially I just have this problem that I'm stuck on, on a sheet about complex numbers: Show that, for ##|r|<1,## $$1+r\cos(x)+r^2\cos(2x)+r^3\cos(3x)...=\frac{1-r\cos(x)}{1-2r\cos(x)+r^2}$$ My first thought was to express it as a geometric series, where the real part of the sum of the series would be the series you see above: $$1+re^{ix}+r^2e^{2ix}+r^3e^{3ix}...$$ The sum of this series is just: $$\frac{(re^{ix})^n-1}{re^{ix} - 1}$$ I'm having some trouble trying to figure out what to...
Back
Top