Potential due to a dipole is given by: V≈4πεor2pcosθ where p: electric dipole moment θ: angle made by the line joining center of dipole and the point with the dipole moment vector r: distance between the center of dipole and the point Note: Approximation is made that the length of dipole is negligible as compared to the distance of the point from the dipole.
Capacitance of parallel plate capacitor with a combination of dielectrics
Example: In the figure shown, find the effective capacitance across P and Q. (Area of each plate is α) Solution: The above arrangement acts as the K1 capacitor in parallel with K2 and K3 which are in series. C1=2dk1ε0α,C2=2dk2ε0α2,C3=2dk3ε0α2 C2 and C3 are in series. Ceff1=C21+C31 Ceff1=k2ε0αd+k3ε0αd=Ceff=dε0α(k2+k3k2k3) C1 is in parallel with Ceff ∴ Total capacitance C=2dk1ε0α+dεoα(k2+k3k2k3) C=dε0α(2k1+k2+k3k2k3)