8.2 Signs of Charges
The force of gravity is always an attractive force, acting to pull one mass toward another. In this photo, the Earth is attracted to the sun.
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨|¨ close=¨|¨»«msub»«mover»«mi»F«/mi»«mo»§#8594;«/mo»«/mover»«mrow»«mi»S«/mi»«mi»u«/mi»«mi»n«/mi»«mo»§#8594;«/mo»«mi»E«/mi»«mi»a«/mi»«mi»r«/mi»«mi»t«/mi»«mi»h«/mi»«/mrow»«/msub»«/mfenced»«mo»=«/mo»«mfrac»«mrow»«mi»G«/mi»«msub»«mi»m«/mi»«mrow»«mi»S«/mi»«mi»u«/mi»«mi»n«/mi»«/mrow»«/msub»«msub»«mi»m«/mi»«mrow»«mi»E«/mi»«mi»a«/mi»«mi»r«/mi»«mi»t«/mi»«mi»h«/mi»«/mrow»«/msub»«/mrow»«mrow»«mi»r«/mi»«mn»2«/mn»«/mrow»«/mfrac»«/math»
An electrostatic force can be an attracting force or a repelling force, depending upon the sign of the charges. In the photo above, the balloons repel each other because each balloon has a negative charge.
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨|¨ close=¨|¨»«msub»«mover»«mi»F«/mi»«mo»§#8594;«/mo»«/mover»«mrow»«mi»b«/mi»«mi»a«/mi»«mi»l«/mi»«mi»l«/mi»«mi»o«/mi»«mi»o«/mi»«mi»n«/mi»«mn»1«/mn»«mo»§#8594;«/mo»«mi»b«/mi»«mi»a«/mi»«mi»l«/mi»«mi»l«/mi»«mi»o«/mi»«mi»o«/mi»«mi»n«/mi»«mn»2«/mn»«/mrow»«/msub»«/mfenced»«mo»=«/mo»«mfrac»«mrow»«mi»k«/mi»«msub»«mi»q«/mi»«mrow»«mi»b«/mi»«mi»a«/mi»«mi»l«/mi»«mi»l«/mi»«mi»o«/mi»«mi»o«/mi»«mi»n«/mi»«mn»1«/mn»«/mrow»«/msub»«msub»«mi»q«/mi»«mrow»«mi»b«/mi»«mi»a«/mi»«mi»l«/mi»«mi»l«/mi»«mi»o«/mi»«mi»o«/mi»«mi»n«/mi»«mn»2«/mn»«/mrow»«/msub»«/mrow»«mrow»«mi»r«/mi»«mn»2«/mn»«/mrow»«/mfrac»«/math»
As implied above, two of the most fundamental laws in physics, which describe completely different phenomena and are based on completely different observations, are very similar. The reasons for these similarities remain a mystery. However, it would be misleading to say that these forces are identical because there are some important differences.
Remember, when you solve problems with Coulomb's law, substitute only the magnitude of the charges into the equation; the signs of the charges are considered after the calculation is complete to determine the direction of the resulting force.
Read Example 10.1Review this example on page 530 in your textbook. |
Complete the "Practice Problem" on page 530 of your textbook.
Given:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»q«/mi»«mi»e«/mi»«/msub»«mo»=«/mo»«mo»-«/mo»«mn»1«/mn»«mo».«/mo»«mn»60«/mn»«mo»§#215;«/mo»«msup»«mn»10«/mn»«mrow»«mo»-«/mo»«mn»19«/mn»«mo»§#160;«/mo»«/mrow»«/msup»«mi»C«/mi»«mspace linebreak=¨newline¨»«/mspace»«msub»«mi»q«/mi»«mi»p«/mi»«/msub»«mo»=«/mo»«mo»+«/mo»«mn»1«/mn»«mo».«/mo»«mn»60«/mn»«mo»§#215;«/mo»«msup»«mn»10«/mn»«mrow»«mo»-«/mo»«mn»19«/mn»«mo»§#160;«/mo»«/mrow»«/msup»«mi»C«/mi»«mspace linebreak=¨newline¨»«/mspace»«mi»r«/mi»«mo»=«/mo»«mn»5«/mn»«mo».«/mo»«mn»29«/mn»«mo»§#215;«/mo»«msup»«mn»10«/mn»«mrow»«mo»-«/mo»«mn»11«/mn»«/mrow»«/msup»«mo»§#160;«/mo»«mi»m«/mi»«/math»
Required:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mover»«mi»F«/mi»«mo»§#8594;«/mo»«/mover»«mi»e«/mi»«/msub»«mo»=«/mo»«mo»?«/mo»«/math»
Analysis and Solution
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mtable columnspacing=¨0px¨ columnalign=¨right center left¨»«mtr»«mtd»«mfenced open=¨|¨ close=¨|¨»«msub»«mover»«mi»F«/mi»«mo»§#8594;«/mo»«/mover»«mi»e«/mi»«/msub»«/mfenced»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mfrac»«mrow»«mi»k«/mi»«msub»«mi»q«/mi»«mi»p«/mi»«/msub»«msub»«mi»q«/mi»«mi»e«/mi»«/msub»«/mrow»«msup»«mi»r«/mi»«mn»2«/mn»«/msup»«/mfrac»«/mtd»«/mtr»«mtr»«mtd»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mfrac»«mrow»«mfenced»«mrow»«mn»8«/mn»«mo».«/mo»«mn»99«/mn»«mo»§#215;«/mo»«msup»«mn»10«/mn»«mn»9«/mn»«/msup»«mstyle displaystyle=¨true¨»«mfrac»«mrow»«mi»N«/mi»«mo»§#183;«/mo»«msup»«mi»m«/mi»«mn»2«/mn»«/msup»«/mrow»«msup»«mi»C«/mi»«mn»2«/mn»«/msup»«/mfrac»«/mstyle»«/mrow»«/mfenced»«mfenced»«mrow»«mn»1«/mn»«mo».«/mo»«mn»6«/mn»«mo»§#215;«/mo»«msup»«mn»10«/mn»«mrow»«mo»-«/mo»«mn»19«/mn»«/mrow»«/msup»«mi»C«/mi»«/mrow»«/mfenced»«mfenced»«mrow»«mn»1«/mn»«mo».«/mo»«mn»6«/mn»«mo»§#215;«/mo»«msup»«mn»10«/mn»«mrow»«mo»-«/mo»«mn»19«/mn»«/mrow»«/msup»«mi»C«/mi»«/mrow»«/mfenced»«/mrow»«msup»«mfenced»«mrow»«mn»5«/mn»«mo».«/mo»«mn»29«/mn»«mo»§#160;«/mo»«mi»x«/mi»«mo»§#160;«/mo»«msup»«mn»10«/mn»«mrow»«mo»-«/mo»«mn»11«/mn»«/mrow»«/msup»«mi»m«/mi»«/mrow»«/mfenced»«mn»2«/mn»«/msup»«/mfrac»«/mtd»«/mtr»«mtr»«mtd»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mn»8«/mn»«mo».«/mo»«mn»22«/mn»«mo»§#215;«/mo»«msup»«mn»10«/mn»«mrow»«mo»-«/mo»«mn»8«/mn»«/mrow»«/msup»«mi»N«/mi»«/mtd»«/mtr»«mtr»«mtd»«/mtd»«mtd»«/mtd»«mtd»«/mtd»«/mtr»«/mtable»«/math»
Note: That the signs of the charges were not substituted into the equation. This is an attractive force since the opposite charges attracts.
Paraphrase:
The electrostatic force of 8.22 × 10 −8 N pulls the electron toward the proton. This same force pulls the proton toward the electron.
Read Example 10.2Sometimes the law of conservation of charge plays a role in Coulomb's law calculations. Review this example on page 531 of your textbook. |
Complete the "Practice Problem" on page 531 of your textbook.
Given
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»q«/mi»«mi»e«/mi»«/msub»«mo»=«/mo»«mo»-«/mo»«mn»3«/mn»«mo».«/mo»«mn»00«/mn»«mo»§#215;«/mo»«msup»«mn»10«/mn»«mrow»«mo»-«/mo»«mn»6«/mn»«/mrow»«/msup»«mo»§#160;«/mo»«mi»C«/mi»«mspace linebreak=¨newline¨»«/mspace»«msub»«mi»q«/mi»«mi»p«/mi»«/msub»«mo»=«/mo»«mo»+«/mo»«mn»2«/mn»«mo».«/mo»«mn»00«/mn»«mo»§#215;«/mo»«msup»«mn»10«/mn»«mrow»«mo»-«/mo»«mn»6«/mn»«/mrow»«/msup»«mo»§#160;«/mo»«mi»C«/mi»«mspace linebreak=¨newline¨»«/mspace»«mi»r«/mi»«mo»=«/mo»«mn»1«/mn»«mo».«/mo»«mn»20«/mn»«mo»§#215;«/mo»«msup»«mn»10«/mn»«mrow»«mo»-«/mo»«mn»1«/mn»«/mrow»«/msup»«mo»§#160;«/mo»«mi»m«/mi»«/math»
Required
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mover»«mi»F«/mi»«mo»§#8594;«/mo»«/mover»«mi»e«/mi»«/msub»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mo»?«/mo»«/math»
Analysis and Solution
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨|¨ close=¨|¨»«msub»«mover»«mi»F«/mi»«mo»§#8594;«/mo»«/mover»«mi»e«/mi»«/msub»«/mfenced»«mo»=«/mo»«mfrac»«mrow»«mi»k«/mi»«msub»«mi»q«/mi»«mi»e«/mi»«/msub»«msub»«mi»q«/mi»«mi»p«/mi»«/msub»«/mrow»«msup»«mi»r«/mi»«mn»2«/mn»«/msup»«/mfrac»«mspace linebreak=¨newline¨»«/mspace»«mfenced open=¨|¨ close=¨|¨»«msub»«mover»«mi»F«/mi»«mo»§#8594;«/mo»«/mover»«mi»e«/mi»«/msub»«/mfenced»«mo»=«/mo»«mfrac»«mrow»«mfenced»«mrow»«mn»8«/mn»«mo».«/mo»«mn»99«/mn»«mo»§#215;«/mo»«msup»«mn»10«/mn»«mn»9«/mn»«/msup»«mstyle displaystyle=¨true¨»«mfrac»«mrow»«mi»N«/mi»«mo»§#183;«/mo»«msup»«mi»m«/mi»«mn»2«/mn»«/msup»«/mrow»«msup»«mi»C«/mi»«mn»2«/mn»«/msup»«/mfrac»«/mstyle»«/mrow»«/mfenced»«mfenced»«mrow»«mn»5«/mn»«mo».«/mo»«mn»00«/mn»«mo»§#215;«/mo»«msup»«mn»10«/mn»«mrow»«mo»-«/mo»«mn»7«/mn»«/mrow»«/msup»«mo»§#160;«/mo»«mi»C«/mi»«/mrow»«/mfenced»«mfenced»«mrow»«mn»5«/mn»«mo».«/mo»«mn»00«/mn»«mo»§#215;«/mo»«msup»«mn»10«/mn»«mrow»«mo»-«/mo»«mn»7«/mn»«/mrow»«/msup»«mo»§#160;«/mo»«mi»C«/mi»«/mrow»«/mfenced»«/mrow»«msup»«mfenced»«mrow»«mn»1«/mn»«mo».«/mo»«mn»20«/mn»«mo»§#215;«/mo»«msup»«mn»10«/mn»«mrow»«mo»-«/mo»«mn»11«/mn»«/mrow»«/msup»«mo»§#160;«/mo»«mi»m«/mi»«/mrow»«/mfenced»«mn»2«/mn»«/msup»«/mfrac»«mspace linebreak=¨newline¨»«/mspace»«mfenced open=¨|¨ close=¨|¨»«msub»«mover»«mi»F«/mi»«mo»§#8594;«/mo»«/mover»«mi»e«/mi»«/msub»«/mfenced»«mo»=«/mo»«mn»1«/mn»«mo».«/mo»«mn»56«/mn»«mo»§#215;«/mo»«msup»«mn»10«/mn»«mrow»«mo»-«/mo»«mn»1«/mn»«/mrow»«/msup»«mo»§#160;«/mo»«mi»N«/mi»«mspace linebreak=¨newline¨»«/mspace»«msub»«mover»«mi»F«/mi»«mo»§#8594;«/mo»«/mover»«mi»e«/mi»«/msub»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mn»1«/mn»«mo».«/mo»«mn»56«/mn»«mo»§#215;«/mo»«msup»«mn»10«/mn»«mrow»«mo»-«/mo»«mn»1«/mn»«/mrow»«/msup»«mo»§#160;«/mo»«mi»N«/mi»«mo»§#160;«/mo»«mo»[«/mo»«mi»r«/mi»«mi»e«/mi»«mi»p«/mi»«mi»u«/mi»«mi»l«/mi»«mi»s«/mi»«mi»i«/mi»«mi»o«/mi»«mi»n«/mi»«mo»]«/mo»«mo»,«/mo»«mo»§#160;«/mo»«mi»sin«/mi»«mi»c«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mi»l«/mi»«mi»i«/mi»«mi»k«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mi»c«/mi»«mi»h«/mi»«mi»a«/mi»«mi»r«/mi»«mi»g«/mi»«mi»e«/mi»«mi»s«/mi»«mo»§#160;«/mo»«mi»r«/mi»«mi»e«/mi»«mi»p«/mi»«mi»e«/mi»«mi»l«/mi»«mspace linebreak=¨newline¨»«/mspace»«/math»
Note that the signs of the charges were not substituted into the equation as we calculated the magnitude.
Paraphrase
The electrostatic force of 1.56 × 10-1 N pulls the electron toward the proton. This same force pulls the proton toward the electron.