Question

Let there be a spherical symmetric charge distribution with charge density varying as r(r) = r₀$\frac{r}{R}$upto r = R and r(r) = 0 for r > R, where r is the distance from the origin. The electric field at on a distance r (r < R) from the origin is given by-

• A. $\frac{\rho_{0}r^{2}}{4\varepsilon_{0}R}$
• B. $\frac{\rho_{0}r}{4\varepsilon_{0}R}$
• C. $\frac{\rho_{0}r^{4}}{\varepsilon_{0}R}$
• D. $\frac{\rho_{0}r^{2}}{\varepsilon_{0}R}$

Answer 1

Answer: (A)

$\frac{\rho_{0}r^{2}}{4\varepsilon_{0}R}$

Answer 2

$\oint$ . $\overrightarrow { \mathrm { ds } }$ = ….(1)

q_in = = $\int _ { 0 } ^ { \mathrm { r } } \rho _ { 0 } \frac { \mathrm { r } } { \mathrm { R } } 4 \pi \mathrm { r } ^ { 2 } \mathrm { dr }$ = $\frac { 4 \pi \rho _ { 0 } } { R }$ $\frac { r ^ { 4 } } { 4 }$

=, from (1)

E.4pr² = $\frac { \pi \rho _ { 0 } r ^ { 4 } } { \varepsilon _ { 0 } R }$ \ E =