A capacitor is constructed of two concentric conducting cylindrical shells. The radius of the inner cylindrical shell is 2.35 10-3 m, and that of the outer shell is 2.49 10-3 m. When the cylinders carry equal and opposite charges of magnitude 1.61 10-10 C, the electric field between the plates has an average magnitude of 3.80 104 V/m and is directed radially outward from the inner shell to the outer shell.

Question

A capacitor is constructed of two concentric conducting cylindrical shells. The radius of the inner cylindrical shell is 2.35 10-3 m, and that of the outer shell is 2.49 10-3 m. When the cylinders carry equal and opposite charges of magnitude 1.61 10-10 C, the electric field between the plates has an average magnitude of 3.80 104 V/m and is directed radially outward from the inner shell to the outer shell. 
Determine the magnitude of the potential difference between the cylindrical shells. 
Determine the capacitance of this capacitor.

drwls · Answer

You will find the formulas that you need here:
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/capcyl.html

In this case, the gap is so narrow compared to the radius that you can get very high accuracy by treating it as a planar capacitor with gap 0.14*10^-3 m. Multiply that by the average E-field between the cylindrical plates, to get the potential difference, 5.32 V .

The capacitance is C = Q/V