What Are the Surface Charge Densities on a Conducting Slab in an Electric Field?

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The discussion focuses on calculating the surface charge densities on the faces of a conducting slab situated in an electric field created by an infinite sheet of charge. The slab has a net charge density of 5 microC/m^2, while the sheet has a charge density of -3 microC/m^2. Participants note that the electric field inside the conductor is zero, leading to the conclusion that one face must have a negative charge and the other a positive charge. Attempts to use the formula E = density / permittivity of free space have led to confusion, with some participants struggling to arrive at the correct surface charge densities. Clarification on the relationship between the charges on the slab's surfaces is sought to resolve the discrepancies in calculations.
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Homework Statement



An infinite sheet of charge, oriented perpendicular to the x-axis, passes through x = 0. It has area density = -3 micro C/m^2. A thick, infinite conducting slab, also oriented perpendicular to the x-axis, occupies the region between x=a and x=b where a = 4 cm and b=5 cm. The conducting slab has a net charge per unit area = 5 microC/m^2. Calulate the surface charge densities on the left hand and right had faces of the conducting slab. You may also find it useful to note the relationship between them.

Homework Equations


E = density / permittivity of free space (epsilon o)
?


The Attempt at a Solution


According to my physics book, since the inside of the conductor has an electric field of zero, one can assume that the charge on the surfaces are negative and positive. I reasoned that the negative charge would like closer to the y-axis whereas the positive charge would lie on the other side. I tried using the formula above, but I'm guessing it is the wrong formula since I cannot get the correct answer this way. I also tried answers such as -3 micro C and +8 micro C to balance out the total charge of 5 micro C. Where am I going wrong?
 
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It would help if I attached the picture! :rolleyes:
 

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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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