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Three point charges are placed on the y-axis: a charge q at y=a, a charge –2q at the origin, and a charge q at y= –a. Such an ar

den301095 [7]

Answer:

electric field Et = kq [1 / (x-a)² -2 / x² + 1 / (x+a)²]

Explanation:

The electric field is a vector, so it must be added as vectors, in this problem both the charges and the calculation point are on the same x-axis so we can work in a single dimension, remembering that the test charge is always positive whereby the direction of the field will depend on the load under analysis, if the field is positive, if the field is negative.

a) Let's write the electric field for each charge and the total field

E = k q /r

With k the Coulomb constant, q the charge and r the distance of the charge to the test point

Et = E1 + E2 + E3

E1 = k q / (x-a)²

E2 = k (-2q) / x²

E3 = k q / (x + a)²

Et = kq [1 / (x-a)² -2 / x² + 1 / (x+a)²]

The direction of the field is along the x axis

b) To use a binomial expansion we must have an expression the form (1-x)⁻ⁿ where x << 1, for this we take factor like x from all the equations

Et = kq/ x² [1 / (1-a/x)² - 2 + 1 / (1+a/x)²]

We use binomial expansion

(1+x)⁻² = 1 -nx + n (n-1) 2! x² +… x << 1

(1-x)⁻² = 1 +nx + n (n-1) 2! x² + ...

They replace in the total field and leaving only the first terms

Et =kq/x² [-2 +(1 +2 a/x + 2 (2-1)/2 (a/x)² +…) + (1 -2 a/x + 2(2-1) /2 (a/x)² +.) ]

Et = kq/x² [a²/x² + a²/x²2] = kq /x² [2 a²/x²]

Et = k q 2a²/x⁴

point charge

Et = k q 1/x²

Dipole

E = k q a/x³

3 0

3 years ago

What type of rock forms due to heating and cooling?

tatuchka [14]

The type of rocks are magma and the igneous rocks.

5 0

3 years ago

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Monitoring cash flow and keeping track of the bottom line of a business are responsibilities for whom?

lina2011 [118]

Answer:
A financial manager.

Explanation:
This is because a financial manager oversees the financial operations of a company. Generally, a financial manager assumes accounting responsibilities for the company. A financial manager is responsible for planning and managing the company's financial resources.

Side note:
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6 0

2 years ago

In creating an accurate scale model of our solar system, Lana placed Earth 1 foot from the Sun. The actual distance from Earth t

miskamm [114]

Pluto would be placed 39.74 feet far from the Sun.

Astronomers use the gap between Earth and the sun, which is ninety-three million miles, as a new unit of measure called the Astronomical Unit.

Map scale refers to the connection (or ratio) between the space on a map and the corresponding distance on the ground. For example, on a 1:one hundred thousand scale map, 1cm at the map equals 1km on the ground.

The distance between the earth and solar, a = around 150 million km, is defined as one Astronomical Unit (AU). The radius of the solar, the solar is around 700,000 km.

Learn more about Astronomical Unit here brainly.com/question/977568

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3 0

2 years ago

Consider what happens at the moment when the block leaves the surface of the globe. Which of the following statements are correc

erma4kov [3.2K]

Answer:

Statement 1 and 3 are correct.

Explanation:

1. The mass moves downward, so the net acceleration of the block is straight downward.

2.The mass is sliding through the globe, so only the force of gravity is acting on the mass which pulls it in downward direction. The force of gravity has two components [mg sin∅] and [mg cos∅].

6 0

3 years ago

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