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soldier1979 [14.2K]
2 years ago
8

I don't understand this QUESTION​

Physics
1 answer:
alex41 [277]2 years ago
6 0

This electric force calculator will enable you to determine the repulsive or attractive force between two static charged particles. Continue reading to get a better understanding of Coulomb's law, the conditions of its validity, and the physical interpretation of the obtained result.

How to use Coulomb's law

Coulomb's law, otherwise known as Coulomb's inverse-square law, describes the electrostatic force acting between two charges. The force acts along the shortest line that joins the charges. It is repulsive if both charges have the same sign and attractive if they have opposite signs.

Coulomb's law is formulated as follows:

F = keq₁q₂/r²

where:

F is the electrostatic force between charges (in Newtons),

q₁ is the magnitude of the first charge (in Coulombs),

q₂ is the magnitude of the second charge (in Coulombs),

r is the shortest distance between the charges (in m),

ke is the Coulomb's constant. It is equal to 8.98755 × 10⁹ N·m²/C². This value is already embedded in the calculator - you don't have to remember it :)

Simply input any three values

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Answer:

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Explanation:

a. What is the magnitude of the net upward force on the sphere as a function of the height z above the disk?

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F = QE

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b. At what height h does the sphere hover?

The sphere hovers at height z = h when the electric force equals the weight of the sphere.

So, F = mg

Qs/2ε₀[1 - z/√(z² + R²)] = mg

when z = h, we have

Qs/2ε₀[1 - h/√(h² + R²)] = mg

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h/√(h² + R²) = 1 - 2mgε₀/Qs

squaring both sides, we have

[h/√(h² + R²)]² = (1 - 2mgε₀/Qs)²

h²/(h² + R²) = (1 - 2mgε₀/Qs)²

cross-multiplying, we have

h² = (1 - 2mgε₀/Qs)²(h² + R²)

expanding the bracket, we have

h² = (1 - 2mgε₀/Qs)²h² + (1 - 2mgε₀/Qs)²R²

collecting like terms, we have

h² - (1 - 2mgε₀/Qs)²h² = (1 - 2mgε₀/Qs)²R²

Factorizing, we have

[1 - (1 - 2mgε₀/Qs)²]h² = (1 - 2mgε₀/Qs)²R²

So, h² =  (1 - 2mgε₀/Qs)²R²/[1 - (1 - 2mgε₀/Qs)²]

taking square-root of both sides, we have

√h² =  √[(1 - 2mgε₀/Qs)²R²/[1 - (1 - 2mgε₀/Qs)²]]

h =  (1 - 2mgε₀/Qs)R/√[1 - (1 - 2mgε₀/Qs)²]

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\huge\mathfrak\red {Answer:}

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