Image charge: point charge and a sphere

[Fu-Kwun Hwang]

What happened when a charge Q is placed at a distance r from the center of an isolated metal sphere (net charge is zero) with radius R.
The following applet shows the field line distribution between charge Q and sphere.
You can drag the charge Q to different location and watch how the field distribution changed!

Red and green circle shown inside the metal are the image charge for this problem.
The electric field inside the metal is zero. All the electric field outside the sphere can be calculated frome elctric field due to charge charge Q and those two image charges.
Because net charge on the sphere is zero, so the sum of those two image charges is zero,too.
The image charge(green) at the center of the sphere is equal to Q*R/r;
The distance between red and green charge is R*R/r;

You can change the situation from isolated sphere to grounded sphere case.
Then, charge will flow to sphere to make the potential become zero.
The net charge will not be zero when the sphere is grounded.
The applet will show electric field, pontential contiur or charge distribution on the surface of the sphere if you click on those checkboxs.
 
If the charge Q is move inside the sphere, then one of the image charge(red) will be located outside the sphere.

You can study many related physics with this applet. I hope you can enjoy it as much as I do.
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Embed a running copy of this simulation
<applet code='users.ntnu.fkh.chargesphere2_pkg.chargesphere2Applet.class' archive='http://www.phy.ntnu.edu.tw/ntnujava/ejsuser/2/ejs_chargesphere2.jar' name='chargesphere21020' id='chargesphere21020' width='675' height='593' mayscript=true><param name='draggable' value='true'></applet>
Embed a running copy link(show simulation in a popuped window)
<a href='http://www.phy.ntnu.edu.tw/ntnujava/msg.php?smfejs=1020' target='smfejs'>Run simulation</a>

Full screen applet or Problem viewing java?Add http://www.phy.ntnu.edu.tw/ to exception site list
Press the Alt key and the left mouse button to drag the applet off the browser and onto the desktop. This work is licensed under a Creative Commons Attribution 2.5 Taiwan License

• Please feel free to post your ideas about how to use the simulation for better teaching and learning.
• Post questions to be asked to help students to think, to explore.
• Upload worksheets as attached files to share with more users.

Let's work together. We can help more users understand physics conceptually and enjoy the fun of learning physics!

[lookang]

Singh, C. (2006). Student understanding of symmetry and Gauss's law of electricity. American Journal of Physics, 74(10), 923-936.
http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=AJPIAS000074000010000923000001&idtype=cvips&gifs=yes

Problem 7 in Appendix B

In Fig. 4, a point charge +Q1 is at the center of an imaginary spherical surface and another point charge +Q2 is outside it. Point P is on the surface of the sphere. Let Φ_S be the net electric flux through the sphere and E _P be the electric field at point P on the sphere. Which one of the following statements is true?

(a) Both charges +Q1 and +Q2 make nonzero contributions to Φ_S but only the charge +Q1 makes a nonzero contribution to E _P.
(b) Both charges +Q1 and +Q2 make nonzero contributions to Φ_S but only the charge +Q2 makes a nonzero contribution to E _P.
(c) Only the charge +Q1makes a nonzero contribution to Φ_S but both charges +Q1 and +Q2 make nonzero contributions to E _P.
(d) Charge +Q1 makes no contribution to Φ_S or E _P.
(e) Charge +Q2 makes no contribution to Φ_S or E _P.

The answer given is (c), based on the applet visualize E field lines and equal Potential lines ,i got (d), any idea what i got wrong?
Oh, i was looking to the wrong thing, i was looking at the E field lines spacing, i should just look at the number for V=Φ and E on the sphere.


in critical examination of the applet, i think the answer is c
i understand how to use the apple now. not to worry.


Maybe to enhance the usability of the applet, create a object to act as the detector so students can explore the readings on a particular position in space? this will promote the attention focusing on what the students in moving on the applet space.
example http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=1602.0