Half the space between two concentricv elecrodes of a sphereical capacitor is filled , as shwon in Fig, with unifrom istropic dielectric with permittively `epsilon`. The charge of the capacitor is `q`. Find the magnitude of the electric field strength between teh electrodes as a function of distance `r` from the curvature centre of teh electrodes.

Explanation

At the interface of the dielectric and vacumm,
`E_(1t) = E_(2t)`
The electric field must be radial and
`E_(1) = E_(2) = (A)/(epsilon_(0) epsilon r^(2)), a lt r lt b`
Now, `q = (A)/(R^(2)) (2pi R^(2)) + (A)/(epsilon R^(2)) (2pi R^(2))`
`= A (1 + (1)/(epsilon)) 2pi`
or, `E_(1) = E_(2) = (q)/(2pi epsilon_(0) R^(2) (1 + epsilon))`