Find Earth's charge using Gauss's Law

AI Thread Summary
The discussion focuses on calculating Earth's total surface charge using Gauss's Law, given an electric field of 163 N/C directed downward. The user attempted to apply the formula Q = EAε₀, substituting the electric field and Earth's radius to find a charge of approximately -735.56 kC. However, the result was deemed incorrect, as it did not meet the required accuracy threshold. The calculations involved using Earth's radius to determine the surface area, but the final answer was still off. The thread highlights the challenges in applying Gauss's Law accurately in this context.
ndoc
Messages
11
Reaction score
0

Homework Statement



The electric field just above the surface of Earth has been measured to typically be 163 N/C pointing downward.

What is the total charge on Earth's surface implied by this measurement?

Homework Equations



∫EdA = Qinside/ɛo


The Attempt at a Solution



I solved this two ways and got the same answer, which is apparently wrong. using Gauss's Law: EA = Q/ɛo => Q=EAɛo = (-163)(4*pi*r^2)ɛo = -735.56 kC
 
Physics news on Phys.org
ndoc said:

Homework Statement



The electric field just above the surface of Earth has been measured to typically be 163 N/C pointing downward.

What is the total charge on Earth's surface implied by this measurement?

Homework Equations



∫EdA = Qinside/ɛo


The Attempt at a Solution



I solved this two ways and got the same answer, which is apparently wrong. using Gauss's Law: EA = Q/ɛo => Q=EAɛo = (-163)(4*pi*r^2)ɛo = -735.56 kC

Earth's radius is about 6.4E6 m so squared is about 41E12 m^2.
 
right so these are my numbers:

4*pi*(-163)*(8.85x10^-12)*(6.37x10^6)^2

but this produces a wrong answer (has to be within about 97% accuracy) of -735562.52C
or -735.56 kC
 
Thread 'Collision of a bullet on a rod-string system: query'

Thread 'Collision of a bullet on a rod-string system: query'

In this question, I have a question. I am NOT trying to solve it, but it is just a conceptual question. Consider the point on the rod, which connects the string and the rod. My question: just before and after the collision, is ANGULAR momentum CONSERVED about this point? Lets call the point which connects the string and rod as P. Why am I asking this? : it is clear from the scenario that the point of concern, which connects the string and the rod, moves in a circular path due to the string...
View full post »
Thread 'A cylinder connected to a hanged mass'

Thread 'A cylinder connected to a hanged mass'

Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
View full post »

Similar threads

Use of imaginary charge vs Gauss' law
Replies
12
Views
889
Gauss' law problem -- Should the field due to both the inside and outside charges be taken into account?
Replies
28
Views
1K
Sheet of charge - theory
Replies
1
Views
881
I Thought I Understood Gauss' Law (Sheets)
Replies
26
Views
2K
No Electric Charges if No Electric Field in Region
Replies
22
Views
2K
Gauss Law- Conducting and Non-conducting cylindrical shells
Replies
8
Views
5K
Gauss' Law applied to this Charged Spherical Shell with a small hole
Replies
10
Views
3K
Determining electric field using gauss's law--different distributions
Replies
3
Views
1K
Electric field at a point inside a non-uniformly charged sphere
Replies
6
Views
1K
Gauss' law and Faraday cage problem
Replies
10
Views
2K

Hot Threads

Recent Insights

Back
Top