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Question 1. (Marks 15)
The figure shows a cross-section through a long,
straight wire with radius r1 and charge
per unit length λ. Co-axial with the wire is a
hollow metal cylinder with internal radius r2 ,
external radius r3 , and a net charge per unit
length 2λ. Use Gauss’s law and appropriate
Gaussian surfaces to find:
(a) where the charges are distributed, and the charge per unit length on each surface,
(b) the electric field at a distance r < r1 from the axis,
(c) the electric field at a distance r1 < r < r2 from the axis,
(d) the electric field at a distance r2 < r < r3 from the axis,
(e) the electric field at a distance r > r3 from the axis, and finally
(f ) plot the electric field as a function of radius from the axis, from r = 0 to r > r3.
Question 2. [Marks 15]
Suppose you have two 3000 F capacitors (initially uncharged) and a 120 V battery.
(a) Calculate the total energy stored in both capacitors if they are connected in series across the
battery. Draw a schematic diagram showing how the capacitors are connected to the battery.
(b) Calculate the total energy stored in both capacitors if they are connected in parallel across the
battery. Draw a schematic diagram showing how the capacitors are connected to the battery.
(c) Now, charge both capacitors to 120 V, then join their two +ve terminals together, and then
connect their free -ve terminals across the battery. Draw a schematic diagram showing how
the capacitors are connected to the battery, and the voltages on all the components just prior
to the final connection being made. After the final connection is made, the capacitors will be
in series with the battery, and current will flow until a new equilibrium is reached. Calculate
the final voltage across each capacitor, and the total energy stored in both capacitors.
