Question

A charge q is situated at the centre of a square of side d. The electric field intensity at the midpoint of a side is E${}_1$ and at one corner of the square is E${}_2$. Then, the ratio of $E_1/E_2$ is :

• A. $0.5$
• B. $0.7$
• C. $1$
• D. $2$

Answer 1

Answer: (D)

$2$

Here, $OP=d/2$ and $PQ=d/2$ so $OQ=\sqrt{O{P}^2+P{Q}^2}=\sqrt{(d/2{)}^2+(d/2{)}^2}=\frac{d}{\sqrt{2}}$
The electric field at P is $E_1=\frac{kq}{O{P}^2}=\frac{4kq}{d^2}$ and
field at Q is $E_2=\frac{kq}{O{Q}^2}=\frac{2kq}{d^2}$
Thus, $\frac{E_1}{E_2}=\frac{4}{2}=2$