Question

Write the formula for electric field and potential due to charged non-conducting

sphere at

(i) Extreme point

(ii) Surface​

Answer 1

To find:

The expression for electrostatic field intensity and electrostatic potential due to a charged non conducting sphere at

• Extremity (i.e. at infinity)

• Surface

Calculation:

General expressions as derived from Gauss' theorem and related application of calculus are as follows:

At infinity :

At infinity , the charge on the non conducting sphere does not exert any effect ; hence the field indices become zero at infinity.

$\boxed{1) \: E_{ \infty} = 0} \\ \\ \boxed{2) \: V_{ \infty} = 0}$

At the surface :

$1) \: E_{(surface)} = \dfrac{kq}{ {r}^{2} }$

$\boxed{ = > \: E_{(surface)} = \dfrac{q}{4\pi \epsilon_{0} {r}^{2} } }$

$2) \: V_{(surface)} = \dfrac{kq}{r}$

$\boxed{ = > \: V_{(surface)} = \dfrac{q}{4\pi \epsilon_{0}r} }$