If the total charge enclosed by a surface is zero, does it imply that the elecric field everywhere on the surface is zero? Conversely, if the electric field everywhere on a surface is zero, does it imply that net charge inside is zero.

Question

If the total charge enclosed by a surface is zero, does it imply that the elecric field everywhere on the surface is zero? Conversely, if the electric field everywhere on a surface is zero, does it imply that net charge inside is zero.,

MARKS App · Accepted Answer

Gauss' law states that $ ∮ s ​ E . dS = ε 0 ​ q ​ T h ee l ec t r i c f i e l d in t h e L H S i s d u e t o a llt h ec ha r g es b o t hin s i d e an d o u t s i d e t h es u r f a ce . T h e t er m \mathrm{q} o n t h er i g h t s i d eo f t h ee q u a t i o n g i v e nb y G a u s s ′ l a w re p rese n t o n l y t h e t o t a l c ha r g e in s i d e an d o u t s i d eo f t h es u r f a ce . S o , d es p i t e b e in g t o t a l c ha r g e in s i d ee n c l ose d b y a sor f a cezero , i t d oes n ′ t im pl y t ha tt h ee l ec t r i c f i e l d e v ery w h ereo n t h es u r f a ce i szero , t h e f i e l d ma y b e n or ma lt o t h es u r f a ce . A l so , i f t h ee l ec t r i c f i e l d e v ery w h ereo na G a u ss ian s u r f a ce i szero , i t d oes n ′ t im pl y t ha t n e t c ha r g e in s i d e i t i szero . I t i s p oss ib l e , o n l y w h e n o u t s i d ec ha r g e w i ll b ezero . i . e . , P u tt in g \mathrm{E}=0 in \oint \mathrm{E} \cdot \mathrm{dS}=\frac{\mathrm{q}}{\varepsilon_0} S o , \quad q=0$.

Search any question & find its solution

Looking for more such questions to practice?