Question

An 'atom' was earlier assumed to be a sphere of radius 'a' having a positively charged point nucleus of charge +Ze at its centre.This nucleus was believed to be surrounded by a uniform density of negative charge that made the atom neutral as a whole.Use the theorem to find the electric field of this 'atom' at a distance r(r<a) from the centre of the atom

Answer 1

Dear student,

for r<a the field will be their .
for r>a the field will be zero.
$$\begin{gathered} forr<a \\ takespaherofradiusr<a \\ thechargeenclosedinthespherebeq=Ze-\frac{Ze}{{\displaystyle \frac{4}{3}}{\mathrm{\pi a}}^3}\times \frac{4}{3}\pi r^3=Ze-\frac{Ze}{{\displaystyle a^3}}{r}^3 \\ sothefieldaccordingtogausslaw \\ E=\frac{q}{{\epsilon }_{0}4{\mathrm{\pi r}}^2}=\frac{Ze\left(1-\frac{r^3}{{\displaystyle a^3}}\right)}{{\epsilon }_{0}4{\mathrm{\pi r}}^2} \\ thiswillbethefieldatthedis\tan cerfromthecenterinsidethesphere. \\ Regards \end{gathered}$$