Two oppositely charged but otherwise identical conductingplates of area 2.50 square centimeters are separated by adielectric 1.80 millimeters thick, with a dielectric constant ofk=3.60. the resultant electric field in the dielectric is1.20 \times 10^{6} volts per meter.
a) compute the magnitude of the charge per unit areasigma on the conducting plate.
b) compute the magnitude of the charge per unit areasigma_1 on the surfaces of the dielectric.
c) find the total electric-field energy u stored in the capacitor.

Now that we have a feel for the state of the circuit in its steady state, let us obtain the expression for the current in the circuit as a function of time. note that we can use the loop rule (going around counterclockwise): e−vr−vl=0. note as well that vr=ir and vl=ldidt. using these equations, we can get, after some rearranging of the variables and making the subsitution x=er−i, dxx=−rldt. integrating both sides of this equation yields x=x0e−rt/l. use this last expression to obtain an expression for i(t). remember that x=er−i and that i0=i(0)=0. express your answer in terms of e, r, and l. you may or may not need all these variables. use the notation exp(x) for ex.