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Example1:The following four charges are located inside a submarine: 5.00 μC, –9.00 μC, 27.0 μC, and –84.0 μC. a) Calculate the net electric flux through the hull of the submarine. b) Is the number of electric field lines leaving the submarine greater than, equal to, or less than the number entering it?
Example2:Consider a long cylindrical charge distribution of radius R with a uniform charge density ρ. Find the electric field at distance r from the axis where r < R.
Example3:Two conducting spheres with diameters of 0.400 m and 1.00 m are separated by a distance that is large compared with the diameters. The spheres are connected by a thin wire and are charged to 7.00 μC. a) How is this total charge shared between the spheres? (Ignore any charge on the wire.) b) What is the potential of the system of spheres when the reference potential is taken to be V = 0 at r = ∞?
Example4:Determine:a) the capacitance andb) the maximum potential difference that can be applied to a Teflon-filled parallel-plate capacitor having a plate area of 1.75 cm2 and plate separation of 0.040 0 mm.
Example5:An electric current is given by the expression I(t) = 100 sin(120πt), where I is in amperes and t is in seconds. What is the total charge carried by the current from t = 0 to t = (1/240) s?
Example6:A conducting rod of length ℓ moves with velocity v parallel to a long wire carrying a steady current I. The axis of the rod is maintained perpendicular to the wire with the near end a distance r away, as shown below. Find the magnitude of the emf induced in the rod.
Example7:Consider an LC circuit in which L = 500 mH and C = 0.100 μF. a) What is the resonance frequency ω0? b) If a resistance of 1.00 kΩ is introduced into this circuit, what is the frequency of the (damped) oscillations?
