Question

$r_1=1m$
$r_2=2m$
$r_3=3m$

Figure shows some equipotential surfaces [Spherical in shape]

• A. Electric field in the region is directed radialy outwards.
• B. Magnitude of electric field is $E=6r$
• C. Magnitude of electric field is $E=\frac{6}{r^2}$
• D. Electric field decreases as we move radialy outwords.

Answer 1

Answer: (A), (B)

Magnitude of electric field is $E=6r$

Let $E=c{r}^n$ by $dV=-\overrightarrow{E}.\overrightarrow{dr}$
${\int }_{10}^{1}dv=-{\int }_1^{2}c{r}^{n}dr\Rightarrow 9=\frac{C}{r+1}(2^{n+1}-1)$ ---(1)
${\int }_{10}^{-14}dv={\int }_1^{3}c{r}^{n}dr\Rightarrow 24=\frac{C}{n+1}(3^{n+1}-1)$ ---(2)
By (2) ÷ (1) $\Rightarrow \frac{8}{3}=\frac{(3^{n+1}-1)}{(2^{n+1}-1)}$
By hit and trial n = 1
By (1) $\Rightarrow 9=\frac{C}{2}(2^2-1)$
C = 6
So E = 6r