How to Calculate Electric Field at the Center of Curvature of a Hemisphere?

In summary, the problem asks to calculate the electric field at the center of curvature of a hemisphere with a uniform surface charge distribution. The surface charge density is given by sigma = Q/(2*PI*r^2) and can be divided into a series of rings, with each ring carrying a charge dQ=sigma*2*PI*dr. At the center of curvature, only the z-component of the electric field is present. To find dE_z, dQ is expressed as sigma dA, where dA is the area in spherical polar coordinates. For half a sphere, the values of theta and phi are known.
  • #1
captainjack2000
99
0

Homework Statement


Charge Q is distributed uniformly over surface of a hemisphere of radius r. Calculate electric field at centre of curvature of hemisphere.


Homework Equations


I realize that this should be quite straightforward but I am a bit confused.
The total charge Q is distributed over surface of hemisphere with surface charge density sigma where
sigma = Q/(2*PI*r^2)
I think you would then divide the hemisphere into a series of rings where each ring would carry a charge
dQ=sigma*2*PI*dr ?

At the centre of curvature the components of electric field perpendicular to the axis will cancel so you will only have electric field along the axis z.

Not quite sure where to go from here.





The Attempt at a Solution

 
Physics news on Phys.org
  • #2
You're correct in saying that there only is a z-component of the field so express dE_z in terms of dE.

You also know that dQ=\sigma dA. What is dA in spherical polar coordinates? What are the values of \theta and \phi for half a sphere?
 
Last edited:

FAQ: How to Calculate Electric Field at the Center of Curvature of a Hemisphere?

What is an electric field in a hemisphere?

The electric field in a hemisphere refers to the force per unit charge experienced by a charged particle placed at any point inside the hemisphere. It is a vector quantity that represents the direction and magnitude of the electric force.

How is the electric field in a hemisphere calculated?

The electric field in a hemisphere can be calculated using the formula E = Q/4πε0R2, where Q is the charge of the hemisphere, ε0 is the permittivity of free space, and R is the radius of the hemisphere.

What factors affect the electric field in a hemisphere?

The electric field in a hemisphere is affected by the charge of the hemisphere, the distance from the center of the hemisphere, and the permittivity of the material surrounding the hemisphere.

How does the electric field vary in a hemisphere?

In a hemisphere, the electric field varies based on the distance from the center of the hemisphere. As the distance increases, the electric field decreases.

What are the applications of electric field in a hemisphere?

The electric field in a hemisphere has various applications, including in electrostatic generators, capacitors, and electron microscopy. It is also used in understanding the behavior of charged particles in electromagnetic fields.

Similar threads

Multipole Expansion for Two Charged Hemispheres
Replies
9
Views
1K
Electric field & force due to charged insulating hemispherical shells
Replies
12
Views
776
The potential of a sphere with opposite hemisphere charge densities
Replies
6
Views
3K
Exploring Electric Field Boundaries at a Charge Density Boundary
Replies
2
Views
2K
Electric Field due to a disk of radius R in the xy-plane
Replies
7
Views
2K
Divergence of the Electric field of a point charge
Replies
13
Views
3K
Using Gauss' law to find the induced surface charge density ##\sigma##
Replies
2
Views
1K
Electrodynamics: Conducting sphere of radius R cut in half
2
Replies
49
Views
5K
Why is the Electric Field of a Polarized Atom Different in Textbooks?
Replies
2
Views
2K
A problem in graphing electric field lines
Replies
17
Views
2K

Hot Threads

Recent Insights

Back
Top