Question

There are three concentric thin sphere of radius a, b, c ( a > b > c ) . the total surface charges densities on their surfaces are $\sigma ,-\sigma ,sigma$ respectively. the magnitude of electric field at r ( distance from centre ) such that a > r > b is :

• A. 0
• B. $\frac{\sigma }{{\epsilon }_0{r}^2}(b^2-c^2)$
• C. $\frac{\sigma }{{\epsilon }_0{r}^2}(a^2+b^2)$
• D. none of these

Answer 1

The correct option is C $\frac{\sigma }{{\epsilon }_0{r}^2}(a^2+b^2)$

Sphere of radius $a,b,c$ $a>b>c$ densities of charges surface $=\sigma ,-\sigma$ sigma respectively.

The magnitude of electric field at $=r$ (distance from centre)

$a>r>b$

Using Gauss law,

$E=\frac{\sigma }{{ϵ}_0{r}^2}(a^2+b^2)$

$V_A=V_C$

$(a-b+c)=\frac{a^2-b^2}{c}+C$

$a-b=\frac{a^2+b^2}{r}$

Now,

$E=\frac{\sigma }{{ϵ}_0{r}^2}(a^2+b^2)$