 Solution

ID: past-exam-of-the-physics-2-paper-of-the-university-of-oxford/2018/7/ii/solution

For

b < r < a

l

encloses net charge

Q

: the sphere and the cavity-wall charge cancel, leaving

+ Q

on the outside of the inner conductor. In the long-cylinder approximation,

E_{r} (r) 2 π r l = \frac{Q}{ϵ _{0}}, E_{r} (r) = \frac{Q}{2 π ϵ _{0} l r} = \frac{2 R V}{l r} .

The electric field points radially outward for

V > 0

. End effects and axial nonuniformity near the openings are excluded by the ideal coaxial cylindrical capacitor approximation.

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