Question

Match the following.

Column - I	Column - II
a) Electric field outside a conducting charged sphere	e) Constant
b)Electric potential outside a conducting charged sphere	f) directly proportional to distance from centre
c) Electric field inside a non-conducting charged sphere	g) inversely proportional to distance from center
d) Electric potential inside a charged conducting sphere	h) inversely proportional to the square of distance from center

• A. a - h, b - g, c - e, d - f
• B. a - e, b - f, c - h, d - g
• C. a - h, b - g, c - f, d - e
• D. a - g, b - h, c - f, d - e

Answer 1

The correct option is C a - h, b - g, c - f, d - e

a ) Electric field outside sphere, take a spherical gaussion surface

$E\times 4\pi r^2=\frac{V}{{\xi }_0}$

$E=\frac{V}{4\pi {\xi }_0{r}^2}\therefore E\propto \frac{1}{r^2}$

b ) Now $E=\frac{KV}{r^2}$

we know $V=-{\int }_d^{r}Edr=-KV[\frac{1}{r}{]}_r=\frac{KV}{r}$

c ) Apply Gauss law taking a sphere at a distance r

we get $E\times 4\pi r^2=\frac{4}{3}\pi r^3\frac{p}{{\xi }_0}$

$E=\frac{Pr}{2\xi }\therefore E\propto r$

d ) Shell Theorem : electric potential inside a changed conducting sphere is constant and is equal to the value at the surface

$\therefore V=constant$