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main points and formulae for electric charges and feilds chapter

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main points and formulae for electric charges and feilds chapter

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Sure! Here are the main points and formulas for the chapter on electric charges and fields:

  1. Electric Charge:

    • Electric charge is a fundamental property of matter.
    • It can be positive or negative.
    • Like charges repel each other, while opposite charges attract.
  2. Coulomb's Law:

    • Coulomb's law states that the force between two point charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them.
    • The formula for Coulomb's law is: F = k * (q1 * q2) / r^2 where F is the force between the charges, q1 and q2 are the magnitudes of the charges, r is the distance between them, and k is the electrostatic constant.
  3. Electric Field:

    • An electric field is a region around a charged object where another charged object experiences a force.
    • The electric field is a vector quantity, meaning it has both magnitude and direction.
    • The formula for electric field due to a point charge is: E = k * (q / r^2) where E is the electric field, q is the magnitude of the charge, r is the distance from the charge, and k is the electrostatic constant.
  4. Electric Field Lines:

    • Electric field lines are imaginary lines used to represent the direction and strength of an electric field.
    • They always point away from positive charges and towards negative charges.
    • The density of electric field lines represents the strength of the field.
  5. Electric Potential:

    • Electric potential is the amount of work done to bring a unit positive charge from infinity to a point in an electric field.
    • It is a scalar quantity and is measured in volts (V).
    • The formula for electric potential due to a point charge is: V = k * (q / r) where V is the electric potential, q is the magnitude of the charge, r is the distance from the charge, and k is the electrostatic constant.

These are the main points and formulas for the chapter on electric charges and fields.

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BackgroundThe electric field ๐ธโ†’ of a particle with charge ๐‘ž can be derived from its electric potential ๐‘‰:๐ธโ†’=โˆ’โˆ‡๐‘‰where โˆ‡ is the derivative operator and ๐‘‰ at every point in space is ๐‘‰=14๐œ‹๐œ€0๐‘ž||๐‘Ÿโ†’||where ๐‘Ÿโ†’ is the distance from the particle at that point, 14๐œ‹๐œ€0 is some constant, and ||๐‘Ÿโ†’||=๐‘Ÿ๐‘ฅ2+๐‘Ÿ๐‘ฆ2 (in a two-dimensional plane). The net electric potential at any point is the sum of all of the electric potentials from all the particles.The force from particle ๐ต on particle ๐ด is the charge of ๐ด (๐‘ž๐ด) multiplied by the electric field from ๐ต: ๐นโ†’๐ตโ†’๐ด=๐‘ž๐ด๐ธโ†’๐ต=14๐œ‹๐œ€0๐‘ž๐ดโ‹…๐‘ž๐ต||๐‘Ÿโ†’||2๐‘Ÿ^For this problem, however, you will only visualize the electric potential ๐‘‰.ProblemGiven two kinds of particles, those with a positive charge +๐‘’, and those with negative charges โˆ’๐‘’, display the electric potential at every point in space. The electric potential should be normalized relative to |๐‘’|4๐œ‹๐œ€0 (i.e., treat |๐‘’|4๐œ‹๐œ€0 as 1).InputInput starts with 3 integers ๐‘›,๐‘š,๐‘ž where 0<๐‘›,๐‘šโ‰ค50 and 0<๐‘žโ‰ค10. Then follows ๐‘ž lines: each line contains three values ๐‘ฅ,๐‘ฆ,๐‘ , where 1โ‰ค๐‘ฅโ‰ค๐‘š and 1โ‰ค๐‘ฆโ‰ค๐‘› correspond to the integer coordinates of the charged particle and ๐‘  is the sign of the particleโ€™s charge being either a + or a -. No two particles will have the same coordinates.OutputYour output should be an ๐‘›ร—๐‘š grid of ASCII characters oriented with the positive ๐‘ฆ-axis pointing down and the positive ๐‘ฅ-axis pointing to the right, with coordinates starting from 1. Every character in the grid corresponds to the total potential at that point.If the field contains a particle, print either a + or - corresponding to its charge. Otherwise, the character you place will be related to the sign of the potential. If the potential is negative then use the characters {%,X,x}. If it is positive, however, use the character set {0,O,o} (the first element is a zero).There are 3 tiers to the fieldโ€™s magnitude:1/๐œ‹1/๐œ‹21/๐œ‹3If the field is below the third tier print a โ€œ.โ€.If the magnitude is above the first tier then you would use % or 0 (zero) depending on the sign, if it is below the first tier then you would use X or O, and so on and so forth.Sample Input 1 Sample Output 120 20 25 5 +15 15 -OOOOOOOOOoooo.......OOOOOOOOOoooo.......OOO000OOOOooo.......OO00000OOOooo.......OO00+00OOOoo........OO00000OOooo........OOO000OOOoo....xxxxxOOOOOOOOoo...xxxxxxxOOOOOOOoo...xxxxxxxxooOOOooo...xxxXXXxxxooooooo...xxXXXXXXXxoooooo...xxXXXXXXXXXoooo....xxXXX%%%XXXX.......xxxXX%%%%%XXX.......xxXXX%%-%%XXX......xxxXXX%%%%%XXX......xxxXXXX%%%XXXX......xxxxXXXXXXXXXX......xxxxXXXXXXXXXX......xxxxxXXXXXXXXxSample Input 2 Sample Output 220 20 315 15 -10 10 +5 5 -XXXXXXXXXXxxxxxxxxxxXXXXXXXXXXxxxxxxxxxxXXX%%%XXXXxxxxxxxxxxXX%%%%%XXXxxxxxxxxxxXX%%-%%XXxxxxxxxxxxxXX%%%%%Xxx..xxxxxxxxXXX%%%Xx.oo..xxxxxxxXXXXXXx.OOOo..xxxxxxXXXXXx.O000Oo.xxxxxxXXXXxxoO0+0OoxxXXXXXxxxxx.oO000O.xXXXXXXxxxxx..oOOO.xXXXXXXXxxxxxx..oo.xX%%%XXXXxxxxxxx..xxX%%%%%XXXxxxxxxxxxxXX%%-%%XXXxxxxxxxxxXXX%%%%%XXXxxxxxxxxxXXXX%%%XXXXxxxxxxxxxXXXXXXXXXXXxxxxxxxxxXXXXXXXXXXXxxxxxxxxxXXXXXXXXXXXSample Input 3 Sample Output 320 20 210 2 +10 18 -oooOOOO00000OOOOoooooooOOOO00+00OOOOoooooooOOOO00000OOOOooooooooOOOO000OOOOooooooooooOOOOOOOOOooooooooooooOOOOOOOoooooo..oooooooOOOooooooo......ooooooooooo.....................................................................xxxxxxxxxxx......xxxxxxxXXXxxxxxxx..xxxxxxXXXXXXXxxxxxx.xxxxxXXXXXXXXXxxxxxxxxxxXXXX%%%XXXXxxxxxxxxXXXX%%%%%XXXXxxxxxxxXXXX%%-%%XXXXxxxxxxxXXXX%%%%%XXXXxxxxxxxXXXXX%%%XXXXXxxxx

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