Question

A point charge is placed at $A(3,4)\text{m}$ in $xy$ plane then electric field at origin is $E$. If charge is moved from $A$ to $B$ $(24,7)\text{m}$ then electric field at origin is:-

• A. $\frac{E}{25}$
  
• B. $25E$
• C. $5E$
• D. $\frac{E}{5}$
  

Answer 1

The correct option is A $\frac{E}{25}$


Distance of origin from the given points,

$r_A=\sqrt{3^2+4^2}=5\text{m}$

and $r_B=\sqrt{(24{)}^2+(7{)}^2}=25\text{m}$

As we know that the electric field is,

$E\propto \frac{1}{{\text{(distance)}}^2}\frac{E_B}{E_A}={\left(\frac{r_A}{r_B}\right)}^2={\left(\frac{5}{25}\right)}^2=\frac{1}{25}$

$\Rightarrow E_B=\frac{E_A}{25}=\frac{E}{25}$