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  • The electric field and charge of a spherical capacitor.
Topics:  Capacitor, capacitance, spherical capacitor, electric field, electrostatics, charge.

Pre-requisite skills: Basic understanding of electrostatics.

Approximate completion time:  Under an hour.

Provide sufficient detail to verify that the assignment was completed in a meaningful manner.

Applet by Wolfgang Christian
In this applet, the two surfaces are held at a constant potential difference, even when the size of the inner surface is resized.

1.  Examine the value of the charges on each surface.  These values represent the maximum value of charge that the capacitor can store.   Now using the mouse, shrink the inner surface to a significantly smaller radius.  

(a) What happens to this maximum charge? 

(b) Explain your result, using

(i) the mathematical relationship between capacitance, potential difference, and charge, 

(ii) basic principles of electrostatic attraction/repulsion.


2. Using the mouse, you can determine the radii of each surface.   Using the displayed data, calculate the capacitance of the capacitor for a given radius.  (Show all work.)


3.   Calculate the maximum charge for this given capacitance and compare it to the displayed value.

When drawing electric field lines from a plot of equipotential lines, a common question is "How far apart should the electric field lines be spaced?"  One rule of thumb that can be used is to use a circle whose diameter reaches from one equipotential line to the next, as shown in the below figure.  (Note:   The equipotential lines must be drawn for a constant increment in value.)  The electric field lines (shown in blue) are drawn so as to perpendicular to the equipotential lines and, at the same time, touch the circle.

Equipotential.gif (3514 bytes)

4.  If equipotential lines are spaced close together, is this indicative of a strong or weak electric field?

5.  Examine the spacing between the equipotential lines for two different radii of the inner surface.

(a) Using your answer to Question 4, which radius corresponds to a stronger electric field?

(b) Explain your answer in terms of the location of the charges on the inner and outer surface. 

Helpful Resources

  1. Physlet Problems: Capacitors by Wolfgang Christian
  2. The Physics Hypertextbook by Glenn Elert (see Capacitance)
  3. P10D - Electricity and Magnetism by Janak Sodha

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