Question

A charge is placed at the centre of a square. If $E_1$ is the electrostatic field due to the charge at the corner of the square and $E_2$ is that at the mid point of the side of the square, then $E_1/E_2$ is

• A. 2
• B. $\frac{1}{2}$
• C. $1/\sqrt{2}$
• D. $\sqrt{2}$

Answer 1

The correct option is B $\frac{1}{2}$

Let the side of the square be $2a$. Then $E_1$ the electrostatic field at $A=\frac{q}{{OA}^2}$
where $q$ is the charge at $O$
But ${OA}^2={OB}^2+{AB}^2=a^2+a^2=2a^2$
$\therefore E_1=\frac{q}{2a^2}$
And $E_2$ the electrostatic field at $B$,
$\frac{q}{{OB}^2}=\frac{q}{a}$
$\therefore \frac{E_1}{E_2}=\frac{\frac{q}{2a^2}}{\frac{q}{a^2}}=\frac{1}{2}$