Answer to Question #280640 in Electricity and Magnetism for Zabibadsha

Question

prove divD= volume charge density using gauss law .Also find the capacitance of two concentric spherical metal shells radii a and b.

Answer 1

$\oint_S\vec D dS=\iiint_V\text{div}\vec Dd V,$

$Q=\int_V\rho dV,$

$\smallint_V\text{div}\vec DdV=\int_V\rho dV,\implies$

$\text{div}\vec D=\rho.$

$U=U_2-U_1=kQ(\frac 1{R_1}-\frac 1{R_2}),$

$C=\frac QU=\frac{R_1R_2}{k(R_2-R_1)}.$