Electrostatic force in a medium of non uniform permittivity

In summary, the problem involves two point charges (+4 μC and -10 μC) placed 10 cm apart in air, with a dielectric slab of large area and thickness 5 cm placed between them. The dielectric has a dielectric constant of 9. The question asks for the force of attraction between the charges. Using the equation F=\frac{1}{4πε}\frac{q_1q_2}{r^2} and the effective permittivity equation ε_{eff}=\frac{ε_r}{1+ε_r\frac{L}{L_{ε_r}}}, we can calculate the effective permittivity as 0.9. Plugging this into the equation F=\frac
  • #1
PhysicoRaj
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Homework Statement


Two point charges, [itex]+4 μC[/itex] and [itex]-10 μC[/itex] are placed 10 cm apart in air. A dielectric slab of large area and thickness 5 cm is placed between the charges. Find the force of attraction between the charges, if the dielectric has a dielectric constant of 9.

Homework Equations


[itex]F=\frac{1}{4πε}\frac{q_1q_2}{r^2}[/itex]

[itex]ε=ε_0{ε_r}[/itex]

The Attempt at a Solution


The electric field exists in a region of non uniform permittivity. Half of the region is free space while the other half is εr=9. Now should I consider the effective permittivity of the space b/n the charges? Or should I calculate the electric fields in the two different media or something like that?
Thanks.
 
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  • #2
Well, I was searching for an equation for effective permittivity and I got it as
[itex]ε_{eff}=\frac{ε_r}{1+ε_r\frac{L}{L_{ε_r}}}[/itex]
Plugging in 9 for [itex]ε_r,[/itex] 5cm each for [itex]L[/itex] and [itex]L_{ε_r},[/itex] I get [itex]ε_{eff}=0.9[/itex]
Now
[itex]\frac{1}{4πε}=\frac{9\times10^9}{ε_{eff}}[/itex][itex]=10^{10}[/itex]

So [itex]F=\frac{10^{10}\times40\times10^{-12}}{(0.1)^2}[/itex]
[itex]F=40N[/itex] and its [itex]wrong[/itex]
 
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  • #3
Anybody please?
 
  • #4
What is the correct answer as per answer key ?
 
  • #5
Ok, I have to search it, its been a long time. Wait..
 
  • #6
They have not given the answer.. there are 4 options: 9N, 11N, 5N, 12N.
 

FAQ: Electrostatic force in a medium of non uniform permittivity

1. What is electrostatic force in a medium of non-uniform permittivity?

Electrostatic force is the attractive or repulsive force between two charged particles in a medium. In a medium of non-uniform permittivity, the permittivity (ability of a material to store electric charge) varies at different points, resulting in a non-uniform distribution of the electrostatic force.

2. How does permittivity affect electrostatic force?

Permittivity is directly related to the strength of the electrostatic force. A higher permittivity means a larger force, while a lower permittivity means a smaller force between charged particles in a medium.

3. What is the formula for calculating electrostatic force in a medium of non-uniform permittivity?

The formula for electrostatic force in a medium of non-uniform permittivity is F = q1q2/4πεr^2, where q1 and q2 are the charges of the two particles, ε is the permittivity of the medium, and r is the distance between the particles.

4. How does the non-uniformity of permittivity affect the strength of electrostatic force?

The non-uniformity of permittivity can lead to a varying distribution of the electrostatic force, resulting in areas of higher or lower force between charged particles in the medium.

5. What are some real-world applications of electrostatic force in a medium of non-uniform permittivity?

Electrostatic force in a medium of non-uniform permittivity plays a crucial role in various technologies, such as capacitors, dielectric materials, and electronic components. It is also important in natural phenomena, such as lightning and atmospheric electricity.

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