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Sidana [21]
3 years ago
7

An electron is placed on a line connecting two fixed point charges of equal charge but the opposite sign. The distance between t

he charges is 30.0 cm and the charge of each is 4.50 pC. (a) Compute the force on the electron at 5.0 cm intervals starting from 5.0 cm from the leftmost charge and ending 5.0 cm from the rightmost charge. (b) Plot the net force versus electron location using your computed values. From the plot, can you make an educated guess as to where the electron feels the least force
Physics
1 answer:
viktelen [127]3 years ago
4 0

Answer:

a)    F_net = 6.48 10⁻¹⁸ ( \frac{1}{x^2} + \frac{1}{(0.300-x)^2} ),   b) x = 0.15 m

Explanation:

a) In this problem we use that the electric force is a vector, that charges of different signs attract and charges of the same sign repel.

The electric force is given by Coulomb's law

         F =k \frac{q_2q_2}{r^2}

         

Since when we have the two negative charges they repel each other and when we fear one negative and the other positive attract each other, the forces point towards the same side, which is why they must be added.

          F_net= ∑ F = F₁ + F₂

let's locate a reference system in the load that is on the left side, the distances are

left side - electron       r₁ = x

right side -electron     r₂ = d-x

let's call the charge of the electron (q) and the fixed charge that has equal magnitude Q

we substitute

          F_net = k q Q  ( \frac{1}{r_1^2}+ \frac{1}{r_2^2})

          F _net = kqQ  ( \frac{1}{x^2} + \frac{1}{(d-x)^2} )

         

let's substitute the values

          F_net = 9 10⁹  1.6 10⁻¹⁹ 4.50 10⁻⁹ ( \frac{1}{x^2} + \frac{1}{(0.30-x)^2} )

          F_net = 6.48 10⁻¹⁸ ( \frac{1}{x^2} + \frac{1}{(0.300-x)^2} )

now we can substitute the value of x from 0.05 m to 0.25 m, the easiest way to do this is in a spreadsheet, in the table the values ​​of the distance (x) and the net force are given

x (m)        F (N)

0.05        27.0 10-16

0.10          8.10 10-16

0.15          5.76 10-16

0.20         8.10 10-16

0.25        27.0 10-16

b) in the adjoint we can see a graph of the force against the distance, it can be seen that it has the shape of a parabola with a minimum close to x = 0.15 m

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*example included* Two uncharged spheres are separated by 3.50 m. If 1.30 ✕ 10¹² electrons are removed from one sphere and place
likoan [24]

Considering the Coulomb's Law, the magnitude of the Coulomb force is 3.1865 N.

<h3>Coulomb's Law</h3>

Charged bodies experience a force of attraction or repulsion on approach.

From Coulomb's Law it is possible to predict what the electrostatic force of attraction or repulsion between two particles will be according to their electric charge and the distance between them.

From Coulomb's Law, the electric force with which two point charges at rest attract or repel each other is directly proportional to the product of the magnitude of both charges and inversely proportional to the square of the distance that separates them:

F=k\frac{Qq}{d^{2} }

where:

  • F is the electrical force of attraction or repulsion. It is measured in Newtons (N).
  • Q and q are the values ​​of the two point charges. They are measured in Coulombs (C).
  • d is the value of the distance that separates them. It is measured in meters (m).
  • K is a constant of proportionality called the Coulomb's law constant. It depends on the medium in which the charges are located. Specifically for vacuum k is approximately 9×10⁹ \frac{Nm^{2} }{C^{2} }.

The force is attractive if the charges are of opposite sign and repulsive if they are of the same sign.

<h3>This case</h3>

In this case, you know that:

  • The two uncharged sphere are separated by the distance of d= 3.50 m
  • The number of electrons are 1.30×10¹².
  • Electrons is elementary charge and charges on both the sphere is same. The value of electron is 1.602×10⁻¹⁹ C. This is, Q=q=1.30×10¹²×1.602×10⁻¹⁹ C= 2.0826×10⁻⁷ C

Replacing in Coulomb's Law:

F=9x10^{9} \frac{Nm^{2} }{C^{2} }\frac{(2.0826x10^{-7} C)x(2.0826x10^{-7} C)}{(3.50 m)^{2} }

Solving:

<u><em>F= 3.1865 N</em></u>

Finally, the magnitude of the Coulomb force is 3.1865 N.

Learn more about Coulomb's Law:

brainly.com/question/26892767

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