9.6 Electric Fields in Two Dimensions
St. Elmo's fire is very difficult to photograph; a camera does not capture the faint blue glow very well, and St. Elmo's fire occurs in circumstances that make photography difficult. A photographer would have to be close to the top of a ship's mast in a thunderstorm or just behind the trailing edge of an aircraft wing in flight!
An alternative is to photograph a phenomenon similar to St. Elmo's fire such as the blue streamers of light visible in the photo of this plasma lamp. While the phenomenon is not St. Elmo's fire, the ribbons of light in a plasma lamp do have many things in common with St. Elmo's fire:
- The effects are due to the presence of strong electric fields.
- The electric fields strip some electrons from gaseous molecules producing a hot, ionized gas called plasma .
- Light is emitted when electrons drop to lower energy levels within atoms.
- The colour of the emitted light depends upon the particular atoms affected.
Because the atmosphere is comprised mostly of nitrogen, the light emitted from St. Elmo's fire is blue, which is the characteristic colour emitted when nitrogen atoms are ionized. The manufacturers of plasma lamps deliberately introduce other gases to produce dramatic effects.
The streamers of light in this close-up photograph of a plasma lamp are particularly beautiful, not only because the colour is so striking but also because of the graceful, twisting shapes. These shapes are caused by charged particles within the streamers that are under the influence of more than one electric field. St. Elmo's fire also involves overlapping electric fields that simultaneously influence many charges.
Read Example 11.3To learn what happens when electric fields with only x components overlap, read from the bottom of page 549 to the end of Example 11.3 on page 550 of the text. As you review the example, identify the key steps and then focus on the details in each step. Afterwards, complete Self-Check 1 to 3. | Read Example 11.4To learn what happens when electric fields are described with both x- and y-components, read Example 11.4 on pages 551 and 552 of your textbook. As you read through this example, first identify the key steps and then focus on the details in each step. Afterwards, complete Self-Check 4 |
Review the previous photo of the plasma lamp. If the charged particles within the streamer were only under the influence of the electric field of the negatively charged central orb, what shape would the streamers have?
If the negatively charged central orb was the only source of electric fields, then the electric field lines would be straight-pointing to the centre of the source. Positive ions would be forced to move along these lines and would be attracted to the source, while electrons would be forced to move along these lines to the outside. In this simplified approach, it follows that the streamers would form straight lines, radiating out from the centre.
Try "Practice Problems" 1 on page 550 of your textbook. For question 2 remember the charge on a proton and electron is equal to the elementary charge on your datasheet.
Given
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Analysis and Solution
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Note that the signs of the charges were not substituted into the equation as we calculated the magnitude.
Paraphrase
The electrostatic field of 3.67 × 10−8 N/C, left.
Try "Practice Problems" 1 on page 550 of your textbook. For question 2 remember the charge on a proton and electron is equal to the elementary charge on your datasheet.
Given
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Required
The electric field halfway between the electron and proton.
Analysis and Solution
Since the magnitude of the charge of the electron and proton is the same, and the distance from each particle to the point is the same, the magnitude of the electric field due to the electron and the proton will be the same.
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Since the charge on the electron is negative, the electric field caused by the electron will be toward the electron. Since the charge on the proton is positive, the electric field caused by the proton will also be toward the electron.
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Paraphrase
The electrostatic field of 3.67 × 10−8 N/C, left.
Do "Practice Problem" 1 on page 551 of your textbook.
Given
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Required
The electric field at point P.
Analysis and Solution
Since q1 and r1 are the same magnitude as q 2 and r 2 , the magnitude of the electric fields will be the same; however, the directions will be different.
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Note that the x-components of «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mover»«mi»E«/mi»«mo»§#8594;«/mo»«/mover»«mn»1«/mn»«/msub»«/math» and «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mover»«mi»E«/mi»«mo»§#8594;«/mo»«/mover»«mn»2«/mn»«/msub»«/math» are in opposite directions but have equal magnitude. Therefore the two cancel each other out.
The resultant electric field at point P is the sum of the y-components.
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Paraphrase
The electric field at point P is 3.43×1012 N/C [90°].