Electrostatic force in a medium of non uniform permittivity

AI Thread Summary
The discussion revolves around calculating the electrostatic force between two point charges, +4 μC and -10 μC, separated by a dielectric slab with a dielectric constant of 9. The electric field is affected by the non-uniform permittivity of the medium, as half of the space is free air and the other half is the dielectric. The user attempts to find the effective permittivity and calculates it as ε_eff = 0.9, leading to a force calculation of 40N, which they believe is incorrect. They seek clarification on the correct method to determine the force and mention the answer options provided, which are 9N, 11N, 5N, and 12N. The discussion highlights the complexities of working with dielectric materials in electrostatics.
PhysicoRaj
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Homework Statement


Two point charges, +4 μC and -10 μC 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


F=\frac{1}{4πε}\frac{q_1q_2}{r^2}

ε=ε_0{ε_r}

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.
 
Last edited:
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Well, I was searching for an equation for effective permittivity and I got it as
ε_{eff}=\frac{ε_r}{1+ε_r\frac{L}{L_{ε_r}}}
Plugging in 9 for ε_r, 5cm each for L and L_{ε_r}, I get ε_{eff}=0.9
Now
\frac{1}{4πε}=\frac{9\times10^9}{ε_{eff}}=10^{10}

So F=\frac{10^{10}\times40\times10^{-12}}{(0.1)^2}
F=40N and its wrong
 
Last edited:
Anybody please?
 
What is the correct answer as per answer key ?
 
Ok, I have to search it, its been a long time. Wait..
 
They have not given the answer.. there are 4 options: 9N, 11N, 5N, 12N.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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