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iris [78.8K]
3 years ago
12

Rearrange the Coulomb's Law formula to find distance(r)

Physics
2 answers:
lesantik [10]3 years ago
6 0
<span>Coulomb's law describes the magnitude of the electrostatic force between two electric charges. The Coulomb's law formula is:
  <span>F = Ke * q1 * q2 / r2</span>

Where:
  q1: Charge of object 1
  q2: Charge of object 2
  r: Distance between the two objects
  F: Force between the two objects. A positive force implies a repulsive interaction, while a negative force implies an attractive interaction
  Ke = Coulomb Constant, 8.9875517873681764 * 109 N.m2.C<span>-2
</span>
Coulomb's Law Examples:
What is the magnitude of the force between two protons which are 1.6E10-6 meters apart?

The charge of 1 proton is +1e (+1.602E-19 C).

F = 8.9875517873681764 * 109 * 1.602E-19 * 1.602E-19 / (1.6E-6 * 1.6 E-6) = 9 * 10-17 N


Source- http://www.endmemo.com/physics/coulomb.php




f = k (q^1)(q^2)/r^2

both sides by r^2 Multiply
fr^2/r^2 = kq^3/r^2

both sides by r^2 divide 
f = kq^3/r^2


Answer:
f = kq^3/r^2



Hope this helps!!!!


</span>
vaieri [72.5K]3 years ago
4 0

Answer:

distance in terms of force is given as

r = \sqrt{\frac{kq_1q_2}{f}}

Explanation:

here as we know that the force between two charges placed at distance "r" is given by Coulomb's law

It is given by the formula

F = \frac{kq_1q_2}{r^2}

now we have to rearrange it for finding the distance

so here we will multiply both sides by square of the distance

f \times r^2 = kq_1q_2

now we will divide both sides force "f"

r^2 = \frac{kq_1q_2}{f}

now square root both sides

r = \sqrt{\frac{kq_1q_2}{f}}

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Complete Question

The complete question is shown on the first uploaded image

Answer:

a

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The producer surplus  is   P = 375

Explanation:

      From the question we are told that

           The inverse market demand is  p_d = p_N -0.1Q

                The inverse supply function is     p_s = 2+ 0.012Q

a

The effect of change in the price  is mathematically given as

                  \frac{\delta p}{\delta p_N}

Now differntiating the inverse market demand function with respect to p_N

We get that  

                   \frac{\delta p}{\delta p_N} =1

b

   We are told that p_N =$30

        Therefore the inverse market demand becomes

                             p_d = 30 -0.1Q

At  equilibrium

                  p_d = p_s

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               30 -0.1Q_e = 2+ 0.012Q_e

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                p_d = 30 - 0.1 (250 )

                    p_d = 5

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     For  Q =  0

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                 p_d = 5

                 p_s = 5

Hence the consumer surplus is mathematically evaluated as

           C = \frac{1}{2} * Q_e * (30 -5)

Substituting value

        C = \frac{1}{2} * 250 (30-5)

           C= 3125

And

  The  producer surplus is mathematically evaluated as

                    P = \frac{1}{2} *250 * (5-2)

                    P = 375

     

         

           

                     

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