(Solved): Problem 5. Fig. 7 presents a system of four parallel thin conducting plane each of area A, separated ...
Problem 5. Fig. 7 presents a system of four parallel thin conducting plane each of area A, separated by some distances and having charges
Q_(1)=8Q,
Q_(2)=3Q,Q_(3)=-4Qand
Q_(4)=Q, where separation distance
d≪\sqrt(A). For numerical answer assume
Q=8.85nC,A=0,5m^(2)and
d=5mm. Based on the principle of superposition: (a) Find the electric field between and outside the plates, as shown in Fig. 7 ( 5 points) (b) Assuming the potential of plate
Q_(4)as a reference (i.e.
V_(4)=V(x_(4))=0) and based on the definition of potential drop
\Delta V=V(x)-V(x_(4))=\int_x^(x_(1)) E(x)dxfind the potentials of the other plates:
V_(1),V_(2)and
V_(3). (5 points) Hint: Based on Problem 4 find the electric fields of charges
Q_(1),Q_(2),Q_(3)and
Q_(4), and apply the principle of superposition. (c) Based on the relationship
\sigma =\epsi _(0)E_(n)obtained in Problem 3, find the charges
Q_(2)^(')and
Q_(2)^('')on the surfaces of the second plate of the system, as it is shown in Fig. 8 (5 points).
